H(x)=20-16x^2+32x

Solution for H(x)=20-16x^2+32x equation:

(H)=20-16H^2+32H

We move all terms to the left:

(H)-(20-16H^2+32H)=0

We get rid of parentheses

16H^2-32H+H-20=0

We add all the numbers together, and all the variables

16H^2-31H-20=0

a = 16; b = -31; c = -20;
Δ = b2-4ac
Δ = -312-4·16·(-20)
Δ = 2241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2241}=\sqrt{9*249}=\sqrt{9}*\sqrt{249}=3\sqrt{249}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-3\sqrt{249}}{2*16}=\frac{31-3\sqrt{249}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+3\sqrt{249}}{2*16}=\frac{31+3\sqrt{249}}{32}
$