H=-5t^2+60t+180

Solution for H=-5t^2+60t+180 equation:

=-5H^2+60H+180

We move all terms to the left:

-(-5H^2+60H+180)=0

We get rid of parentheses

5H^2-60H-180=0

a = 5; b = -60; c = -180;
Δ = b2-4ac
Δ = -602-4·5·(-180)
Δ = 7200
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:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60\sqrt{2}}{2*5}=\frac{60-60\sqrt{2}}{10}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60\sqrt{2}}{2*5}=\frac{60+60\sqrt{2}}{10}
$