G(5)=3x^2+2x-1

Solution for G(5)=3x^2+2x-1 equation:

(5)=3G^2+2G-1

We move all terms to the left:

(5)-(3G^2+2G-1)=0

We get rid of parentheses

-3G^2-2G+1+5=0

We add all the numbers together, and all the variables

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

a = -3; b = -2; c = +6;
Δ = b2-4ac
Δ = -22-4·(-3)·6
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{19}}{2*-3}=\frac{2-2\sqrt{19}}{-6}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{19}}{2*-3}=\frac{2+2\sqrt{19}}{-6}
$