H=1600t-16t^2

Solution for H=1600t-16t^2 equation:

=1600H-16H^2

We move all terms to the left:

-(1600H-16H^2)=0

We get rid of parentheses

16H^2-1600H=0

a = 16; b = -1600; c = 0;
Δ = b2-4ac
Δ = -16002-4·16·0
Δ = 2560000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2560000}=1600$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1600)-1600}{2*16}=\frac{0}{32}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1600)+1600}{2*16}=\frac{3200}{32}
=100
$