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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


6x/18x^2+(-3x)/18x^2-2-1=0

We add all the numbers together, and all the variables

6x/18x^2+(-3x)/18x^2-3=0

We multiply all the terms by the denominator


6x+(-3x)-3*18x^2=0

Wy multiply elements

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

We get rid of parentheses

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