H(x)=-6x^2+384

Solution for H(x)=-6x^2+384 equation:

(H)=-6H^2+384

We move all terms to the left:

(H)-(-6H^2+384)=0

We get rid of parentheses

6H^2+H-384=0

a = 6; b = 1; c = -384;
Δ = b2-4ac
Δ = 12-4·6·(-384)
Δ = 9217
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{9217}}{2*6}=\frac{-1-\sqrt{9217}}{12}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{9217}}{2*6}=\frac{-1+\sqrt{9217}}{12}
$