Let 7x^2 + 5x = h - x^2 + x. What value of h will give us exactly one solution for x?
7x^2 + 5x = -x^2 + x + h rearrange as
8x^2 + 4x - h = 0
If we have only one solution, the discriminant = 0.....so....
4^2 - 4 (-h)(8) = 0
16 + 32h = 0
32h = -16
h = -16/32 = -1/2