x-3=2/3x

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

x-3=2/3x

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x-2/3x-3=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2-9x-2=0

a = 3; b = -9; c = -2;
Δ = b2-4ac
Δ = -92-4·3·(-2)
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*3}=\frac{9-\sqrt{105}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{105}}{2*3}=\frac{9+\sqrt{105}}{6}
$