H=80t-8t2

Solution for H=80t-8t2 equation:

=80H-8H^2

We move all terms to the left:

-(80H-8H^2)=0

We get rid of parentheses

8H^2-80H=0

a = 8; b = -80; c = 0;
Δ = b2-4ac
Δ = -802-4·8·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-80}{2*8}=\frac{0}{16}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+80}{2*8}=\frac{160}{16}
=10
$