H=-16t^2+84t

Solution for H=-16t^2+84t equation:

=-16H^2+84H

We move all terms to the left:

-(-16H^2+84H)=0

We get rid of parentheses

16H^2-84H=0

a = 16; b = -84; c = 0;
Δ = b2-4ac
Δ = -842-4·16·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-84}{2*16}=\frac{0}{32}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+84}{2*16}=\frac{168}{32}
=5+1/4
$