The creation of equity was necessary in order to make the fixed and rigid common law, more flexible and fair. In ancient England, at certain situations individuals had to seek for ‘more’ to gain justice. Wealthy people, who had more bargaining power, used to bribe the jury and obtained favorable judgments, in certain scenarios common law remedies were an inadequate set of remedies to gain justice, and according to the writ system some litigants could not get an opportunity to take legal actions against another at all, because of the unavailability of a suitable writ. So the people who failed to do justice in common law petitioned the King. King realized the need of a set of rules which was different from the writ system, which provides better, suitable remedies depending on the situation and where jury has no part to play. All these petitions were considered and heard by the Lord Chancellor in the Court of Chancery. This is how equity was created and known as the law of Court of Chancery.
The development of law of equity started to create a conflict with common law as the litigants seek to rely on equitable remedy restricting the order given by the common law courts. Sir Edward Coke chief justice of King’s Bench didn’t like the way the common law is treated and decided imprisonment of for disobedience to injunctions was unlawful  .This conflict raised and further got worse in the case Earl of Oxford  where a judgement of Sir Edward Coke was purportedly get hold by fraud. An injunction was issued prohibiting the enforcement of the decision of common law courts by the court of chancery. Thus this decision dead locked the two courts and eventually the problem was taken to the attorney general Sir Francis Bacon. He decided in favour of the chancery and upheld use of common injunctions deciding that in any circumstance of conflict between common law and equity law, equity would prevail. Thereafter it is said Equity had come , not to destroy the law but to full fill it. 
In order to understand how the law of equity practices and how it supplements the common law it is essential to be familiar with the principle of trusts in modern law of equity as it’s the most distinctive achievement performed by Englishmen in the field of jurisprudence according to Professor Maitland. The essence of a trust is the imposition of an equitable obligation on a person (trustee) which requires that person to act in good conscience when dealing with that property in favour of any person (the beneficiary) who has a beneficial interest recognised by equity in the property.  According to the trust came in to existence it can be categorised as express trust, resulting trust and constructive trust. It is necessary to go in to the detail as how these trusts help to supplement the short comings of common law.
Constructive trust can be defined as arising whenever the circumstances are such that it could be unconscionable for the owner of the legal title to assert his own beneficial interest and deny the beneficial interest of another.  This can be explained by an example as in the case Hammond v Mitchell  where there was a couple unmarried and house was on the man’s name and she was told that this was for the tax reasons and when we are married half will be yours anyway. She relied on this and left her job and helped him in his business. But later they didn’t get married and she was told to leave the home being unconscionable. She had to rely on an equitable remedy as according to the common law it recognises only the legal title owner has the interest on property whereas in equity acquisition of a beneficial interest in the home under the common intention and the detrimental reliance head,  she was granted a half share although she didn’t contribute to the purchase price. The same types of examples can be seen in the cases Grant v Edwards  and Eves v Eves  as how the modern equity supplement the shortcomings of common law.
Secret trust- another constructive trust which can be explained as a trust where a physical evidence is not available to the public but a trustee is appointed in order to carry out testator’s secret intentions. In case McCormick v Grogan  is a classic case which shows the secret trustee tries to commit fraud when carrying out testator’s intentions as he gave his entire estate to a friend Mr. Grogan and gave out the instructions as how it should be divided among his friends and relatives. This case principally explains that law of equity restrict a statute to be used to execute fraud as the secret trustee tried to use section 9 of Wills Act 1837 in common law to claim that he should take constructively to benefit himself but equity would not allow this.
It is vital to observe equitable remedies when considering how equity supplements the inadequacy of common law. Claimants in most cases seek for equitable remedy since the common law only allows damages thus in some cases damages are not really sufficient and the characteristics such as they are discretionary where as the common law remedy is available as of a right, they are granted where the common law remedies would be inadequate or where the common law remedies are not available as the right is exclusively equitable and they act in personam, means against the defendant personally.  Variety of equitable remedies such as Injunctions, specific performance, rescission and rectification are practiced for this purpose.
Specific performance is an order of the court which compels a defendant to carry out their obligations under a contract in accordance with the terms and conditions set out in the contract.  In the case Cooperative insurance society v Argyll Stores  where the specific performance was sought out of an undertaking to keep a supermarket open during the usual business hours of business in a lease which had 19 years to run as its in the middle of a shopping centre ,its closure will adversely affect to the rest of the centre  . It can be clearly seen the legal remedy in this case to shut the supermarket and pay for the damages equitable remedy is as such. When issuing an order for specific performance the factors such as damages must not be an adequate, requirement of mutuality, the exercise of discretion and Equity will not assist a volunteer take into consideration to prevent claimants form unconscionable acts of defendants and to supplement the shortcoming of common law.
It is also necessary to consider another important remedy in equity which is called an Injunction order and accordance with the purpose it can be classified either as prohibitory or mandatory. Prohibitary injunctions are used to restrain a breach of negative undertaking as in the case of Nordenfelt v Maxim Nordenfeltguns  where a machine gun manufacturer after selling his business to the plaintiff with an agreement not to carry on trade for 25 and not adhering to the agreement. Also in American Cyanamid Co v Ethicon  there was an application for an injunction to prevent infringement of a patent. In common law for these types of breach only damages can be awarded and it is a difficult task to measure the damage in the similar kind of cases where as in equity the unconscionable work of the defendant can be stopped.
Other equitable remedies are rectification and Rescission. Rectification is defined as when a written document does not accord with the actual intentions of the parties it can be made by an order.  According to the case Craddock v Hunt  an adjacent yard which belonged to another house was conveyed with the house and held that the conveyance would be rectified to exclude the yard which show the equitable remedy affects on the substance of claimants rights and not merely on the manner of their enforcement as in common law. 
It should be noted that an equitable remedy may fulfil a task of enabling the claimant to take full advantage of a right at common law. A claimant may, for instance, have a right to rescind a contact for fraud, but may be at common law unable to exercise that right because a precise restitutio in integrum is not possible. Equity has a wider discretion to rescind in such a case by developing a reasonable, if not an accurate, return of the parties to something approaching their original positions as in the case of Wood v Scarth  .