H(2)=-6x2+18x+36

Solution for H(2)=-6x2+18x+36 equation:

(2)=-6H^2+18H+36

We move all terms to the left:

(2)-(-6H^2+18H+36)=0

We get rid of parentheses

6H^2-18H-36+2=0

We add all the numbers together, and all the variables

6H^2-18H-34=0

a = 6; b = -18; c = -34;
Δ = b2-4ac
Δ = -182-4·6·(-34)
Δ = 1140
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:

$\sqrt{\Delta}=\sqrt{1140}=\sqrt{4*285}=\sqrt{4}*\sqrt{285}=2\sqrt{285}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{285}}{2*6}=\frac{18-2\sqrt{285}}{12}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{285}}{2*6}=\frac{18+2\sqrt{285}}{12}
$