Let $7x^2 + 5x = h.$ what value of $h$ will give us exactly one solution for $x$?

Try not to use non-standard notation such as " $ " Instead, use commas and/or put each quantity on its own, separate line.

7x^2 + 5x = h can be rewritten as 7x^2 + 5x - h = 0. Then a=7, b=5 and c= -h.

The "discriminant" is b^2 - 4ac. If the discrim. is zero, then the quadratic equation will have TWO (not just one) real, equal roots.

Form b^2-4ac and set it = to 0. Then solve this equation for h:

5^2 - 4(7)(-h) = 0 becomes 25 + 28h = 0. Solving for h, h = -25/28.

If the discriminant is larger than 0, then the quadratic equation will have TWO real, different roots. If smaller than 0, then the q. e. will have two complex roots.

36 is the final answer! : )