H=-16t^2+800t+5

Solution for H=-16t^2+800t+5 equation:

=-16H^2+800H+5

We move all terms to the left:

-(-16H^2+800H+5)=0

We get rid of parentheses

16H^2-800H-5=0

a = 16; b = -800; c = -5;
Δ = b2-4ac
Δ = -8002-4·16·(-5)
Δ = 640320
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:

$\sqrt{\Delta}=\sqrt{640320}=\sqrt{64*10005}=\sqrt{64}*\sqrt{10005}=8\sqrt{10005}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-800)-8\sqrt{10005}}{2*16}=\frac{800-8\sqrt{10005}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-800)+8\sqrt{10005}}{2*16}=\frac{800+8\sqrt{10005}}{32}
$