H=-16t^2+72t+520

Solution for H=-16t^2+72t+520 equation:

=-16H^2+72H+520

We move all terms to the left:

-(-16H^2+72H+520)=0

We get rid of parentheses

16H^2-72H-520=0

a = 16; b = -72; c = -520;
Δ = b2-4ac
Δ = -722-4·16·(-520)
Δ = 38464
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:

$\sqrt{\Delta}=\sqrt{38464}=\sqrt{64*601}=\sqrt{64}*\sqrt{601}=8\sqrt{601}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{601}}{2*16}=\frac{72-8\sqrt{601}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{601}}{2*16}=\frac{72+8\sqrt{601}}{32}
$