H=-16t^2-24t+200

Solution for H=-16t^2-24t+200 equation:

=-16H^2-24H+200

We move all terms to the left:

-(-16H^2-24H+200)=0

We get rid of parentheses

16H^2+24H-200=0

a = 16; b = 24; c = -200;
Δ = b2-4ac
Δ = 242-4·16·(-200)
Δ = 13376
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:

$\sqrt{\Delta}=\sqrt{13376}=\sqrt{64*209}=\sqrt{64}*\sqrt{209}=8\sqrt{209}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{209}}{2*16}=\frac{-24-8\sqrt{209}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{209}}{2*16}=\frac{-24+8\sqrt{209}}{32}
$