3x-2=3(2/3-x)

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

3x-2=3(2/3-x)

We move all terms to the left:

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


Domain of the equation: 3-x))!=0

We move all terms containing x to the left, all other terms to the right

-x))!=-3

x!=-3/1

x!=-3

x∈R


We add all the numbers together, and all the variables

3x-(3(-1x+2/3))-2=0

We multiply all the terms by the denominator


3x*3))-(3(-1x+2-2*3))=0

We add all the numbers together, and all the variables

3x*3))-(3(-1x-4))=0

We add all the numbers together, and all the variables

-1x+3x*3))-(3(=0

Wy multiply elements

9x^2-1x=0

a = 9; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·9·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*9}=\frac{0}{18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*9}=\frac{2}{18}
=1/9
$