2-2x=2/3x-2

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

2-2x=2/3x-2

We move all terms to the left:

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


Domain of the equation: 3x-2)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2+6x+6x-2=0

We add all the numbers together, and all the variables

-6x^2+12x-2=0

a = -6; b = 12; c = -2;
Δ = b2-4ac
Δ = 122-4·(-6)·(-2)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{6}}{2*-6}=\frac{-12-4\sqrt{6}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{6}}{2*-6}=\frac{-12+4\sqrt{6}}{-12}
$