2/3*x-1=1-x

Solution for 2/3*x-1=1-x equation:

2/3x-1=1-x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2-3x-3x+2=0

We add all the numbers together, and all the variables

3x^2-6x+2=0

a = 3; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·3·2
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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