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

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

=-16H^2-16H+180

We move all terms to the left:

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

We get rid of parentheses

16H^2+16H-180=0

a = 16; b = 16; c = -180;
Δ = b2-4ac
Δ = 162-4·16·(-180)
Δ = 11776
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:

$\sqrt{\Delta}=\sqrt{11776}=\sqrt{256*46}=\sqrt{256}*\sqrt{46}=16\sqrt{46}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16\sqrt{46}}{2*16}=\frac{-16-16\sqrt{46}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16\sqrt{46}}{2*16}=\frac{-16+16\sqrt{46}}{32}
$