H=-16t2+200

Solution for H=-16t2+200 equation:

=-16H^2+200

We move all terms to the left:

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

We get rid of parentheses

16H^2-200=0

a = 16; b = 0; c = -200;
Δ = b2-4ac
Δ = 02-4·16·(-200)
Δ = 12800
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:

$\sqrt{\Delta}=\sqrt{12800}=\sqrt{6400*2}=\sqrt{6400}*\sqrt{2}=80\sqrt{2}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{2}}{2*16}=\frac{0-80\sqrt{2}}{32}
=-\frac{80\sqrt{2}}{32}
=-\frac{5\sqrt{2}}{2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{2}}{2*16}=\frac{0+80\sqrt{2}}{32}
=\frac{80\sqrt{2}}{32}
=\frac{5\sqrt{2}}{2}
$