H=5(6t-t2)

Solution for H=5(6t-t2) equation:

=5(6H-H2)

We move all terms to the left:

-(5(6H-H2))=0

We add all the numbers together, and all the variables

-(5(+6H-1H^2))=0


We calculate terms in parentheses: -(5(+6H-1H^2)), so:

5(+6H-1H^2)

We multiply parentheses

-5H^2+30H

Back to the equation:

-(-5H^2+30H)


We get rid of parentheses

5H^2-30H=0

a = 5; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·5·0
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*5}=\frac{0}{10}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*5}=\frac{60}{10}
=6
$