H(t)=-16t^2+192+112

Solution for H(t)=-16t^2+192+112 equation:

(H)=-16H^2+192+112

We move all terms to the left:

(H)-(-16H^2+192+112)=0

We get rid of parentheses

16H^2+H-192-112=0

We add all the numbers together, and all the variables

16H^2+H-304=0

a = 16; b = 1; c = -304;
Δ = b2-4ac
Δ = 12-4·16·(-304)
Δ = 19457
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{-(1)-\sqrt{19457}}{2*16}=\frac{-1-\sqrt{19457}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{19457}}{2*16}=\frac{-1+\sqrt{19457}}{32}
$