H=-16t^2+118t+15

Solution for H=-16t^2+118t+15 equation:

=-16H^2+118H+15

We move all terms to the left:

-(-16H^2+118H+15)=0

We get rid of parentheses

16H^2-118H-15=0

a = 16; b = -118; c = -15;
Δ = b2-4ac
Δ = -1182-4·16·(-15)
Δ = 14884
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14884}=122$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-118)-122}{2*16}=\frac{-4}{32}
=-1/8
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-118)+122}{2*16}=\frac{240}{32}
=7+1/2
$