(2/3x)+3=x

Solution for (2/3x)+3=x equation:

(2/3x)+3=x

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

-1x+(+2/3x)+3=0

We get rid of parentheses

-1x+2/3x+3=0

We multiply all the terms by the denominator


-1x*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}
$