H(x)=-16x^2+56x+96

Solution for H(x)=-16x^2+56x+96 equation:

(H)=-16H^2+56H+96

We move all terms to the left:

(H)-(-16H^2+56H+96)=0

We get rid of parentheses

16H^2-56H+H-96=0

We add all the numbers together, and all the variables

16H^2-55H-96=0

a = 16; b = -55; c = -96;
Δ = b2-4ac
Δ = -552-4·16·(-96)
Δ = 9169
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{-(-55)-\sqrt{9169}}{2*16}=\frac{55-\sqrt{9169}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{9169}}{2*16}=\frac{55+\sqrt{9169}}{32}
$