G(x)=6x/x+2

Solution for G(x)=6x/x+2 equation:

(G)=6G/G+2

We move all terms to the left:

(G)-(6G/G+2)=0


Domain of the equation: G+2)!=0

G∈R


We get rid of parentheses

G-6G/G-2=0

We multiply all the terms by the denominator


G*G-6G-2*G=0

We add all the numbers together, and all the variables

-8G+G*G=0

Wy multiply elements

G^2-8G=0

a = 1; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·1·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*1}=\frac{0}{2}
=0
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*1}=\frac{16}{2}
=8
$