H=32t-16t^2-7

Solution for H=32t-16t^2-7 equation:

=32H-16H^2-7

We move all terms to the left:

-(32H-16H^2-7)=0

We get rid of parentheses

16H^2-32H+7=0

a = 16; b = -32; c = +7;
Δ = b2-4ac
Δ = -322-4·16·7
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{-(-32)-24}{2*16}=\frac{8}{32}
=1/4
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+24}{2*16}=\frac{56}{32}
=1+3/4
$