H=50(5t)-5(5t)^2

Solution for H=50(5t)-5(5t)^2 equation:

=50(5H)-5(5H)^2

We move all terms to the left:

-(50(5H)-5(5H)^2)=0

We get rid of parentheses

55H^2-505H=0

a = 55; b = -505; c = 0;
Δ = b2-4ac
Δ = -5052-4·55·0
Δ = 255025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{255025}=505$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-505)-505}{2*55}=\frac{0}{110}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-505)+505}{2*55}=\frac{1010}{110}
=9+2/11
$