2x-2=1/3x+1

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

2x-2=1/3x+1

We move all terms to the left:

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


Domain of the equation: 3x+1)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-3x-6x-1=0

We add all the numbers together, and all the variables

6x^2-9x-1=0

a = 6; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·6·(-1)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{105}}{2*6}=\frac{9-\sqrt{105}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{105}}{2*6}=\frac{9+\sqrt{105}}{12}
$