G(x)=-x^2-8x-6

Solution for G(x)=-x^2-8x-6 equation:

(G)=-G^2-8G-6

We move all terms to the left:

(G)-(-G^2-8G-6)=0

We get rid of parentheses

G^2+8G+G+6=0

We add all the numbers together, and all the variables

G^2+9G+6=0

a = 1; b = 9; c = +6;
Δ = b2-4ac
Δ = 92-4·1·6
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{57}}{2*1}=\frac{-9-\sqrt{57}}{2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{57}}{2*1}=\frac{-9+\sqrt{57}}{2}
$