H(x)=-4x^2+8

Solution for H(x)=-4x^2+8 equation:

(H)=-4H^2+8

We move all terms to the left:

(H)-(-4H^2+8)=0

We get rid of parentheses

4H^2+H-8=0

a = 4; b = 1; c = -8;
Δ = b2-4ac
Δ = 12-4·4·(-8)
Δ = 129
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{129}}{2*4}=\frac{-1-\sqrt{129}}{8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{129}}{2*4}=\frac{-1+\sqrt{129}}{8}
$