G(0)=x^2-5x+6

Solution for G(0)=x^2-5x+6 equation:

(0)=G^2-5G+6

We move all terms to the left:

(0)-(G^2-5G+6)=0

We add all the numbers together, and all the variables

-(G^2-5G+6)=0

We get rid of parentheses

-G^2+5G-6=0

We add all the numbers together, and all the variables

-1G^2+5G-6=0

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