3x=2x/3x

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

3x=2x/3x

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3x-2x/3x=0

We multiply all the terms by the denominator


3x*3x-2x=0

We add all the numbers together, and all the variables

-2x+3x*3x=0

Wy multiply elements

9x^2-2x=0

a = 9; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·9·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*9}=\frac{0}{18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*9}=\frac{4}{18}
=2/9
$