H=-16t^2-10t+200

Solution for H=-16t^2-10t+200 equation:

=-16H^2-10H+200

We move all terms to the left:

-(-16H^2-10H+200)=0

We get rid of parentheses

16H^2+10H-200=0

a = 16; b = 10; c = -200;
Δ = b2-4ac
Δ = 102-4·16·(-200)
Δ = 12900
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:

$\sqrt{\Delta}=\sqrt{12900}=\sqrt{100*129}=\sqrt{100}*\sqrt{129}=10\sqrt{129}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{129}}{2*16}=\frac{-10-10\sqrt{129}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{129}}{2*16}=\frac{-10+10\sqrt{129}}{32}
$