We want to find the value of $X$ in the given situation.
The sum of the first 20 positive even integers can be found using the formula:
Sum = $n(n + 1)$, where $n$ is the number of terms.
For the first 20 positive even integers, $n = 20$, so we have:
Sum of even integers = $20(20 + 1)$ = $20(21)$ = 420
The sum of the first $X$ positive odd integers can also be found using the formula:
Sum = $n^2$, where $n$ is the number of terms.
Therefore, the sum of the first $X$ positive odd integers is $X^2$.
We are given that the positive difference between these two sums is 195, so we can write:
$420 - X^2 = 195$
Simplifying, we have:
$X^2 = 420 - 195$
$X^2 = 225$
To find the value of $X$, we can take the square root of both sides of the equation:
$X = \sqrt{225}$
Taking the square root of 225 gives us two possible values, +15 and -15. However, since we are looking for the number of positive odd integers, $X$ must be a positive value.
Therefore, the value of $X$ is 15.
The answer is: 15
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
What is the positive difference between the sum of the first 20 positive even integers and the sum of the first X positive odd integers?
If we know the answer to the above question is 195, what is the value of unknown variable X?

### Answer:
