I need to know what x is
I suppose the missed sign is plus.
sqrt(2x+1) - 1 = sqrt(x-4).
Note that x must be >=4 and apply square to both sides:
1 + (2x+1) - 2*sqrt(2x+1) = x-4, or
2*sqrt(2x+1) = x+6. Again apply square:
4*(2x+1) = x^2 + 12x + 36, or
x^2 + 4x + 32 = 0.
The discriminant is 16-4*32 < 0, so there are no solutions.
Also look at the graphs: https://www.desmos.com/calculator/dir0zulvxt
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