H=-16t^2+512t

Solution for H=-16t^2+512t equation:

=-16H^2+512H

We move all terms to the left:

-(-16H^2+512H)=0

We get rid of parentheses

16H^2-512H=0

a = 16; b = -512; c = 0;
Δ = b2-4ac
Δ = -5122-4·16·0
Δ = 262144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{262144}=512$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-512)-512}{2*16}=\frac{0}{32}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-512)+512}{2*16}=\frac{1024}{32}
=32
$