H=-16t2+8t+15

Solution for H=-16t2+8t+15 equation:

=-16H^2+8H+15

We move all terms to the left:

-(-16H^2+8H+15)=0

We get rid of parentheses

16H^2-8H-15=0

a = 16; b = -8; c = -15;
Δ = b2-4ac
Δ = -82-4·16·(-15)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-32}{2*16}=\frac{-24}{32}
=-3/4
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+32}{2*16}=\frac{40}{32}
=1+1/4
$