H=-16t^2+33t+82

Solution for H=-16t^2+33t+82 equation:

=-16H^2+33H+82

We move all terms to the left:

-(-16H^2+33H+82)=0

We get rid of parentheses

16H^2-33H-82=0

a = 16; b = -33; c = -82;
Δ = b2-4ac
Δ = -332-4·16·(-82)
Δ = 6337
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{-(-33)-\sqrt{6337}}{2*16}=\frac{33-\sqrt{6337}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{6337}}{2*16}=\frac{33+\sqrt{6337}}{32}
$