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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3G^2+4G-1=0

a = -3; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·(-3)·(-1)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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