I need to know what x is

Hello!

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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