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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·(-2)·(-3)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-1}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+1}{2*-2}=\frac{-4}{-4}
=1
$