Question

When is 2 x -3 equal to x squared minus 5

Answer 1

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.