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

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

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

We move all terms to the left:

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

We calculate fractions


(-108x^2)/72x^2+24x/72x^2+(-60x)/72x^2-2=0

We multiply all the terms by the denominator


(-108x^2)+24x+(-60x)-2*72x^2=0

Wy multiply elements

(-108x^2)-144x^2+24x+(-60x)=0

We get rid of parentheses

-108x^2-144x^2+24x-60x=0

We add all the numbers together, and all the variables

-252x^2-36x=0

a = -252; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·(-252)·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*-252}=\frac{0}{-504}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*-252}=\frac{72}{-504}
=-1/7
$