G(x)=6x^2+11x+3

Solution for G(x)=6x^2+11x+3 equation:

(G)=6G^2+11G+3

We move all terms to the left:

(G)-(6G^2+11G+3)=0

We get rid of parentheses

-6G^2+G-11G-3=0

We add all the numbers together, and all the variables

-6G^2-10G-3=0

a = -6; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·(-6)·(-3)
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{7}}{2*-6}=\frac{10-2\sqrt{7}}{-12}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{7}}{2*-6}=\frac{10+2\sqrt{7}}{-12}
$