G(x)=-3x^2-12x-9

Solution for G(x)=-3x^2-12x-9 equation:

(G)=-3G^2-12G-9

We move all terms to the left:

(G)-(-3G^2-12G-9)=0

We get rid of parentheses

3G^2+12G+G+9=0

We add all the numbers together, and all the variables

3G^2+13G+9=0

a = 3; b = 13; c = +9;
Δ = b2-4ac
Δ = 132-4·3·9
Δ = 61
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{-(13)-\sqrt{61}}{2*3}=\frac{-13-\sqrt{61}}{6}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{61}}{2*3}=\frac{-13+\sqrt{61}}{6}
$