2/3x-2=3x-2

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

2/3x-2=3x-2

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-9x^2+6x-6x+2=0

We add all the numbers together, and all the variables

-9x^2+2=0

a = -9; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-9)·2
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*-9}=\frac{0-6\sqrt{2}}{-18}
=-\frac{6\sqrt{2}}{-18}
=-\frac{\sqrt{2}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*-9}=\frac{0+6\sqrt{2}}{-18}
=\frac{6\sqrt{2}}{-18}
=\frac{\sqrt{2}}{-3}
$