H(T)=-16t2+72t+24

Solution for H(T)=-16t2+72t+24 equation:

()=-16H^2+72H+24

We move all terms to the left:

()-(-16H^2+72H+24)=0

We add all the numbers together, and all the variables

-(-16H^2+72H+24)=0

We get rid of parentheses

16H^2-72H-24=0

a = 16; b = -72; c = -24;
Δ = b2-4ac
Δ = -722-4·16·(-24)
Δ = 6720
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6720}=\sqrt{64*105}=\sqrt{64}*\sqrt{105}=8\sqrt{105}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{105}}{2*16}=\frac{72-8\sqrt{105}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{105}}{2*16}=\frac{72+8\sqrt{105}}{32}
$