H(t)=16t^2+192t+17

Solution for H(t)=16t^2+192t+17 equation:

(H)=16H^2+192H+17

We move all terms to the left:

(H)-(16H^2+192H+17)=0

We get rid of parentheses

-16H^2+H-192H-17=0

We add all the numbers together, and all the variables

-16H^2-191H-17=0

a = -16; b = -191; c = -17;
Δ = b2-4ac
Δ = -1912-4·(-16)·(-17)
Δ = 35393
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{-(-191)-\sqrt{35393}}{2*-16}=\frac{191-\sqrt{35393}}{-32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-191)+\sqrt{35393}}{2*-16}=\frac{191+\sqrt{35393}}{-32}
$