H=-16t^2+84t+100

Solution for H=-16t^2+84t+100 equation:

=-16H^2+84H+100

We move all terms to the left:

-(-16H^2+84H+100)=0

We get rid of parentheses

16H^2-84H-100=0

a = 16; b = -84; c = -100;
Δ = b2-4ac
Δ = -842-4·16·(-100)
Δ = 13456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13456}=116$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-116}{2*16}=\frac{-32}{32}
=-1
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+116}{2*16}=\frac{200}{32}
=6+1/4
$