H=-16t^2+160t+64

Solution for H=-16t^2+160t+64 equation:

=-16H^2+160H+64

We move all terms to the left:

-(-16H^2+160H+64)=0

We get rid of parentheses

16H^2-160H-64=0

a = 16; b = -160; c = -64;
Δ = b2-4ac
Δ = -1602-4·16·(-64)
Δ = 29696
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:

$\sqrt{\Delta}=\sqrt{29696}=\sqrt{1024*29}=\sqrt{1024}*\sqrt{29}=32\sqrt{29}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-32\sqrt{29}}{2*16}=\frac{160-32\sqrt{29}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+32\sqrt{29}}{2*16}=\frac{160+32\sqrt{29}}{32}
$