H=-8t^2+32t

Solution for H=-8t^2+32t equation:

=-8H^2+32H

We move all terms to the left:

-(-8H^2+32H)=0

We get rid of parentheses

8H^2-32H=0

a = 8; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·8·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*8}=\frac{0}{16}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*8}=\frac{64}{16}
=4
$