H=16t^2+16t=32

Solution for H=16t^2+16t=32 equation:

=16H^2+16H=32

We move all terms to the left:

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

We get rid of parentheses

-16H^2-16H=0

a = -16; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-16)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-16}=\frac{0}{-32}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-16}=\frac{32}{-32}
=-1
$