I believe that the answer to the square root of x^2 + 3x = x-3 is X = 3, x=-3 but I'm not sure. I believe the answer to the square root of 8x -2 = the square root of 2x is x=2 again I'm not sure.

Square both sides of your equation.

It breaks down quite nicely, but remember that you must verify your answer anytime you squared your equation.