H=-4t^2-80t

Solution for H=-4t^2-80t equation:

=-4H^2-80H

We move all terms to the left:

-(-4H^2-80H)=0

We get rid of parentheses

4H^2+80H=0

a = 4; b = 80; c = 0;
Δ = b2-4ac
Δ = 802-4·4·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-80}{2*4}=\frac{-160}{8}
=-20
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+80}{2*4}=\frac{0}{8}
=0
$