H=-16t^2+24t+15

Solution for H=-16t^2+24t+15 equation:

=-16H^2+24H+15

We move all terms to the left:

-(-16H^2+24H+15)=0

We get rid of parentheses

16H^2-24H-15=0

a = 16; b = -24; c = -15;
Δ = b2-4ac
Δ = -242-4·16·(-15)
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-16\sqrt{6}}{2*16}=\frac{24-16\sqrt{6}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+16\sqrt{6}}{2*16}=\frac{24+16\sqrt{6}}{32}
$