H=3t(10-t)

Solution for H=3t(10-t) equation:

=3H(10-H)

We move all terms to the left:

-(3H(10-H))=0

We add all the numbers together, and all the variables

-(3H(-1H+10))=0


We calculate terms in parentheses: -(3H(-1H+10)), so:

3H(-1H+10)

We multiply parentheses

-3H^2+30H

Back to the equation:

-(-3H^2+30H)


We get rid of parentheses

3H^2-30H=0

a = 3; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·3·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*3}=\frac{0}{6}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*3}=\frac{60}{6}
=10
$