H=8+8t-16t^2

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

=8+8H-16H^2

We move all terms to the left:

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

We get rid of parentheses

16H^2-8H-8=0

a = 16; b = -8; c = -8;
Δ = b2-4ac
Δ = -82-4·16·(-8)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-24}{2*16}=\frac{-16}{32}
=-1/2
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+24}{2*16}=\frac{32}{32}
=1
$