1/3x+2=3/6x-4

Solution for 1/3x+2=3/6x-4 equation:

1/3x+2=3/6x-4

We move all terms to the left:

1/3x+2-(3/6x-4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x-4)!=0

x∈R


We get rid of parentheses

1/3x-3/6x+4+2=0

We calculate fractions


6x/18x^2+(-9x)/18x^2+4+2=0

We add all the numbers together, and all the variables

6x/18x^2+(-9x)/18x^2+6=0

We multiply all the terms by the denominator


6x+(-9x)+6*18x^2=0

Wy multiply elements

108x^2+6x+(-9x)=0

We get rid of parentheses

108x^2+6x-9x=0

We add all the numbers together, and all the variables

108x^2-3x=0

a = 108; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·108·0
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*108}=\frac{0}{216}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*108}=\frac{6}{216}
=1/36
$