G(x)=x2-5x+2

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

(G)=G2-5G+2

We move all terms to the left:

(G)-(G2-5G+2)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1G^2+6G-2=0

a = -1; b = 6; c = -2;
Δ = b2-4ac
Δ = 62-4·(-1)·(-2)
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{-(6)-2\sqrt{7}}{2*-1}=\frac{-6-2\sqrt{7}}{-2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{7}}{2*-1}=\frac{-6+2\sqrt{7}}{-2}
$