H=-16t^2-82t

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

=-16H^2-82H

We move all terms to the left:

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

We get rid of parentheses

16H^2+82H=0

a = 16; b = 82; c = 0;
Δ = b2-4ac
Δ = 822-4·16·0
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-82}{2*16}=\frac{-164}{32}
=-5+1/8
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+82}{2*16}=\frac{0}{32}
=0
$