H=-16t^2+64t+50

Solution for H=-16t^2+64t+50 equation:

=-16H^2+64H+50

We move all terms to the left:

-(-16H^2+64H+50)=0

We get rid of parentheses

16H^2-64H-50=0

a = 16; b = -64; c = -50;
Δ = b2-4ac
Δ = -642-4·16·(-50)
Δ = 7296
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:

$\sqrt{\Delta}=\sqrt{7296}=\sqrt{64*114}=\sqrt{64}*\sqrt{114}=8\sqrt{114}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{114}}{2*16}=\frac{64-8\sqrt{114}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{114}}{2*16}=\frac{64+8\sqrt{114}}{32}
$