2/3+1/3x=1/2x+3

Solution for 2/3+1/3x=1/2x+3 equation:

2/3+1/3x=1/2x+3

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


2x/54x^2+(-27x)/54x^2+4x/54x^2-3=0

We multiply all the terms by the denominator


2x+(-27x)+4x-3*54x^2=0

We add all the numbers together, and all the variables

6x+(-27x)-3*54x^2=0

Wy multiply elements

-162x^2+6x+(-27x)=0

We get rid of parentheses

-162x^2+6x-27x=0

We add all the numbers together, and all the variables

-162x^2-21x=0

a = -162; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-162)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*-162}=\frac{0}{-324}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-162}=\frac{42}{-324}
=-7/54
$