2/3x-1/12=5/6x

Solution for 2/3x-1/12=5/6x equation:

2/3x-1/12=5/6x

We move all terms to the left:

2/3x-1/12-(5/6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(+5/6x)-1/12=0

We get rid of parentheses

2/3x-5/6x-1/12=0

We calculate fractions


(-108x^2)/216x^2+144x/216x^2+(-180x)/216x^2=0

We multiply all the terms by the denominator


(-108x^2)+144x+(-180x)=0

We get rid of parentheses

-108x^2+144x-180x=0

We add all the numbers together, and all the variables

-108x^2-36x=0

a = -108; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·(-108)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*-108}=\frac{0}{-216}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*-108}=\frac{72}{-216}
=-1/3
$