2x-4-2/3x=4/3x-4

Solution for 2x-4-2/3x=4/3x-4 equation:

2x-4-2/3x=4/3x-4

We move all terms to the left:

2x-4-2/3x-(4/3x-4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

2x-2/3x-4/3x+4-4=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x*3x+4*3x-4*3x-6=0

Wy multiply elements

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

We add all the numbers together, and all the variables

6x^2-6=0

a = 6; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·6·(-6)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*6}=\frac{12}{12}
=1
$