H=-0.05x^2-20x

Solution for H=-0.05x^2-20x equation:

=-0.05H^2-20H

We move all terms to the left:

-(-0.05H^2-20H)=0

We get rid of parentheses

0.05H^2+20H=0

a = 0.05; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·0.05·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*0.05}=\frac{-40}{0.1}
=-400
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*0.05}=\frac{0}{0.1}
=0
$