G(2)=3x2-5x+1

Solution for G(2)=3x2-5x+1 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -3; b = 5; c = +1;
Δ = b2-4ac
Δ = 52-4·(-3)·1
Δ = 37
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{-(5)-\sqrt{37}}{2*-3}=\frac{-5-\sqrt{37}}{-6}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{37}}{2*-3}=\frac{-5+\sqrt{37}}{-6}
$