H=-16t2+85t+50

Solution for H=-16t2+85t+50 equation:

=-16H^2+85H+50

We move all terms to the left:

-(-16H^2+85H+50)=0

We get rid of parentheses

16H^2-85H-50=0

a = 16; b = -85; c = -50;
Δ = b2-4ac
Δ = -852-4·16·(-50)
Δ = 10425
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:

$\sqrt{\Delta}=\sqrt{10425}=\sqrt{25*417}=\sqrt{25}*\sqrt{417}=5\sqrt{417}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-85)-5\sqrt{417}}{2*16}=\frac{85-5\sqrt{417}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+5\sqrt{417}}{2*16}=\frac{85+5\sqrt{417}}{32}
$