H=5t(9-t)

Solution for H=5t(9-t) equation:

=5H(9-H)

We move all terms to the left:

-(5H(9-H))=0

We add all the numbers together, and all the variables

-(5H(-1H+9))=0


We calculate terms in parentheses: -(5H(-1H+9)), so:

5H(-1H+9)

We multiply parentheses

-5H^2+45H

Back to the equation:

-(-5H^2+45H)


We get rid of parentheses

5H^2-45H=0

a = 5; b = -45; c = 0;
Δ = b2-4ac
Δ = -452-4·5·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-45}{2*5}=\frac{0}{10}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+45}{2*5}=\frac{90}{10}
=9
$