3/6x+3=2/3x

Solution for 3/6x+3=2/3x equation:

3/6x+3=2/3x

We move all terms to the left:

3/6x+3-(2/3x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/6x-(+2/3x)+3=0

We get rid of parentheses

3/6x-2/3x+3=0

We calculate fractions


9x/18x^2+(-12x)/18x^2+3=0

We multiply all the terms by the denominator


9x+(-12x)+3*18x^2=0

Wy multiply elements

54x^2+9x+(-12x)=0

We get rid of parentheses

54x^2+9x-12x=0

We add all the numbers together, and all the variables

54x^2-3x=0

a = 54; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·54·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*54}=\frac{0}{108}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*54}=\frac{6}{108}
=1/18
$