G(x)=x2-6X+8

Solution for G(x)=x2-6X+8 equation:

(G)=G2-6G+8

We move all terms to the left:

(G)-(G2-6G+8)=0

We add all the numbers together, and all the variables

-(+G^2-6G+8)+G=0

We get rid of parentheses

-G^2+6G+G-8=0

We add all the numbers together, and all the variables

-1G^2+7G-8=0

a = -1; b = 7; c = -8;
Δ = b2-4ac
Δ = 72-4·(-1)·(-8)
Δ = 17
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{-(7)-\sqrt{17}}{2*-1}=\frac{-7-\sqrt{17}}{-2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{17}}{2*-1}=\frac{-7+\sqrt{17}}{-2}
$