G(x)=2/3x

Solution for G(x)=2/3x equation:

(G)=2/3G

We move all terms to the left:

(G)-(2/3G)=0


Domain of the equation: 3G)!=0

G!=0/1

G!=0

G∈R


We add all the numbers together, and all the variables

G-(+2/3G)=0

We get rid of parentheses

G-2/3G=0

We multiply all the terms by the denominator


G*3G-2=0

Wy multiply elements

3G^2-2=0

a = 3; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·3·(-2)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*3}=\frac{0-2\sqrt{6}}{6}
=-\frac{2\sqrt{6}}{6}
=-\frac{\sqrt{6}}{3}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*3}=\frac{0+2\sqrt{6}}{6}
=\frac{2\sqrt{6}}{6}
=\frac{\sqrt{6}}{3}
$