H(x)=-16x^2+64+16

Solution for H(x)=-16x^2+64+16 equation:

(H)=-16H^2+64+16

We move all terms to the left:

(H)-(-16H^2+64+16)=0

We get rid of parentheses

16H^2+H-64-16=0

We add all the numbers together, and all the variables

16H^2+H-80=0

a = 16; b = 1; c = -80;
Δ = b2-4ac
Δ = 12-4·16·(-80)
Δ = 5121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5121}=\sqrt{9*569}=\sqrt{9}*\sqrt{569}=3\sqrt{569}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{569}}{2*16}=\frac{-1-3\sqrt{569}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{569}}{2*16}=\frac{-1+3\sqrt{569}}{32}
$