H=-16t^2+24t+1300

Solution for H=-16t^2+24t+1300 equation:

=-16H^2+24H+1300

We move all terms to the left:

-(-16H^2+24H+1300)=0

We get rid of parentheses

16H^2-24H-1300=0

a = 16; b = -24; c = -1300;
Δ = b2-4ac
Δ = -242-4·16·(-1300)
Δ = 83776
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:

$\sqrt{\Delta}=\sqrt{83776}=\sqrt{64*1309}=\sqrt{64}*\sqrt{1309}=8\sqrt{1309}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{1309}}{2*16}=\frac{24-8\sqrt{1309}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{1309}}{2*16}=\frac{24+8\sqrt{1309}}{32}
$