H=-16t^2+31t+2

Solution for H=-16t^2+31t+2 equation:

=-16H^2+31H+2

We move all terms to the left:

-(-16H^2+31H+2)=0

We get rid of parentheses

16H^2-31H-2=0

a = 16; b = -31; c = -2;
Δ = b2-4ac
Δ = -312-4·16·(-2)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-33}{2*16}=\frac{-2}{32}
=-1/16
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+33}{2*16}=\frac{64}{32}
=2
$