H=-12t^2+432t

Solution for H=-12t^2+432t equation:

=-12H^2+432H

We move all terms to the left:

-(-12H^2+432H)=0

We get rid of parentheses

12H^2-432H=0

a = 12; b = -432; c = 0;
Δ = b2-4ac
Δ = -4322-4·12·0
Δ = 186624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{186624}=432$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-432)-432}{2*12}=\frac{0}{24}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-432)+432}{2*12}=\frac{864}{24}
=36
$