H(t)=-16t^2+112.8t+8.5

Solution for H(t)=-16t^2+112.8t+8.5 equation:

(H)=-16H^2+112.8H+8.5

We move all terms to the left:

(H)-(-16H^2+112.8H+8.5)=0

We get rid of parentheses

16H^2-112.8H+H-8.5=0

We add all the numbers together, and all the variables

16H^2-111.8H-8.5=0

a = 16; b = -111.8; c = -8.5;
Δ = b2-4ac
Δ = -111.82-4·16·(-8.5)
Δ = 13043.24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-111.8)-\sqrt{13043.24}}{2*16}=\frac{111.8-\sqrt{13043.24}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-111.8)+\sqrt{13043.24}}{2*16}=\frac{111.8+\sqrt{13043.24}}{32}
$