G(x)=4-2/3x

Solution for G(x)=4-2/3x equation:

(G)=4-2/3G

We move all terms to the left:

(G)-(4-2/3G)=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+4)=0

We get rid of parentheses

G+2/3G-4=0

We multiply all the terms by the denominator


G*3G-4*3G+2=0

Wy multiply elements

3G^2-12G+2=0

a = 3; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·3·2
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{30}}{2*3}=\frac{12-2\sqrt{30}}{6}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{30}}{2*3}=\frac{12+2\sqrt{30}}{6}
$