Solve: 2x - 3 = x^2 - 5 (at least, this is my interpretation of your 2 x -3).
x^2 - 5 - 2x + 3 + 0, or x^2 - 2x - 2 = 0
I will solve this by "completing the square:"
x^2 - 2x +(1)^2 - (1)^2 - 2 = 0, or x^2 - 2x + 1 - 1 - 2 = 0
This is (x-1)^2 = 3. Taking the sqrt of both sides, we get:
x-1 = plus or minus sqrt(3). Then x=1+sqrt(3) or x=1-sqrt(3). These are the two values of x for which 2x - 3 = x^2 - 5 is true.