H=8+64t-16t^2

Solution for H=8+64t-16t^2 equation:

=8+64H-16H^2

We move all terms to the left:

-(8+64H-16H^2)=0

We get rid of parentheses

16H^2-64H-8=0

a = 16; b = -64; c = -8;
Δ = b2-4ac
Δ = -642-4·16·(-8)
Δ = 4608
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:

$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-48\sqrt{2}}{2*16}=\frac{64-48\sqrt{2}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+48\sqrt{2}}{2*16}=\frac{64+48\sqrt{2}}{32}
$