H=-3t(-4t+8)

Solution for H=-3t(-4t+8) equation:

=-3H(-4H+8)

We move all terms to the left:

-(-3H(-4H+8))=0


We calculate terms in parentheses: -(-3H(-4H+8)), so:

-3H(-4H+8)

We multiply parentheses

12H^2-24H

Back to the equation:

-(12H^2-24H)


We get rid of parentheses

-12H^2+24H=0

a = -12; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-12)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-12}=\frac{-48}{-24}
=+2
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-12}=\frac{0}{-24}
=0
$