H=-125t2+500t

Solution for H=-125t2+500t equation:

=-125H^2+500H

We move all terms to the left:

-(-125H^2+500H)=0

We get rid of parentheses

125H^2-500H=0

a = 125; b = -500; c = 0;
Δ = b2-4ac
Δ = -5002-4·125·0
Δ = 250000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{250000}=500$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-500}{2*125}=\frac{0}{250}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+500}{2*125}=\frac{1000}{250}
=4
$