H=100t-50t^2

Solution for H=100t-50t^2 equation:

=100H-50H^2

We move all terms to the left:

-(100H-50H^2)=0

We get rid of parentheses

50H^2-100H=0

a = 50; b = -100; c = 0;
Δ = b2-4ac
Δ = -1002-4·50·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-100}{2*50}=\frac{0}{100}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+100}{2*50}=\frac{200}{100}
=2
$