H=-3t^2+6t+24

Solution for H=-3t^2+6t+24 equation:

=-3H^2+6H+24

We move all terms to the left:

-(-3H^2+6H+24)=0

We get rid of parentheses

3H^2-6H-24=0

a = 3; b = -6; c = -24;
Δ = b2-4ac
Δ = -62-4·3·(-24)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18}{2*3}=\frac{-12}{6}
=-2
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*3}=\frac{24}{6}
=4
$