H=-16t^2-24t+180

Solution for H=-16t^2-24t+180 equation:

=-16H^2-24H+180

We move all terms to the left:

-(-16H^2-24H+180)=0

We get rid of parentheses

16H^2+24H-180=0

a = 16; b = 24; c = -180;
Δ = b2-4ac
Δ = 242-4·16·(-180)
Δ = 12096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12096}=\sqrt{576*21}=\sqrt{576}*\sqrt{21}=24\sqrt{21}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24\sqrt{21}}{2*16}=\frac{-24-24\sqrt{21}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24\sqrt{21}}{2*16}=\frac{-24+24\sqrt{21}}{32}
$