H=-16t^2+96t+16

Solution for H=-16t^2+96t+16 equation:

=-16H^2+96H+16

We move all terms to the left:

-(-16H^2+96H+16)=0

We get rid of parentheses

16H^2-96H-16=0

a = 16; b = -96; c = -16;
Δ = b2-4ac
Δ = -962-4·16·(-16)
Δ = 10240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10240}=\sqrt{1024*10}=\sqrt{1024}*\sqrt{10}=32\sqrt{10}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-32\sqrt{10}}{2*16}=\frac{96-32\sqrt{10}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+32\sqrt{10}}{2*16}=\frac{96+32\sqrt{10}}{32}
$