H=-16t^2+48t+288

Solution for H=-16t^2+48t+288 equation:

=-16H^2+48H+288

We move all terms to the left:

-(-16H^2+48H+288)=0

We get rid of parentheses

16H^2-48H-288=0

a = 16; b = -48; c = -288;
Δ = b2-4ac
Δ = -482-4·16·(-288)
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-144}{2*16}=\frac{-96}{32}
=-3
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+144}{2*16}=\frac{192}{32}
=6
$