H=-16t^2+92t+24

Solution for H=-16t^2+92t+24 equation:

=-16H^2+92H+24

We move all terms to the left:

-(-16H^2+92H+24)=0

We get rid of parentheses

16H^2-92H-24=0

a = 16; b = -92; c = -24;
Δ = b2-4ac
Δ = -922-4·16·(-24)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-100}{2*16}=\frac{-8}{32}
=-1/4
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+100}{2*16}=\frac{192}{32}
=6
$