H=-16t^2+85t+5

Solution for H=-16t^2+85t+5 equation:

=-16H^2+85H+5

We move all terms to the left:

-(-16H^2+85H+5)=0

We get rid of parentheses

16H^2-85H-5=0

a = 16; b = -85; c = -5;
Δ = b2-4ac
Δ = -852-4·16·(-5)
Δ = 7545
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-85)-\sqrt{7545}}{2*16}=\frac{85-\sqrt{7545}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+\sqrt{7545}}{2*16}=\frac{85+\sqrt{7545}}{32}
$