H(4)=-x2+20x

Solution for H(4)=-x2+20x equation:

(4)=-H2+20H

We move all terms to the left:

(4)-(-H2+20H)=0

We add all the numbers together, and all the variables

-(-1H^2+20H)+4=0

We get rid of parentheses

1H^2-20H+4=0

We add all the numbers together, and all the variables

H^2-20H+4=0

a = 1; b = -20; c = +4;
Δ = b2-4ac
Δ = -202-4·1·4
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{6}}{2*1}=\frac{20-8\sqrt{6}}{2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{6}}{2*1}=\frac{20+8\sqrt{6}}{2}
$