H=4t(50-t)

Solution for H=4t(50-t) equation:

=4H(50-H)

We move all terms to the left:

-(4H(50-H))=0

We add all the numbers together, and all the variables

-(4H(-1H+50))=0


We calculate terms in parentheses: -(4H(-1H+50)), so:

4H(-1H+50)

We multiply parentheses

-4H^2+200H

Back to the equation:

-(-4H^2+200H)


We get rid of parentheses

4H^2-200H=0

a = 4; b = -200; c = 0;
Δ = b2-4ac
Δ = -2002-4·4·0
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-200}{2*4}=\frac{0}{8}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+200}{2*4}=\frac{400}{8}
=50
$