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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


(-72x^2)/108x^2+54x/108x^2+(-90x)/108x^2-2=0

We multiply all the terms by the denominator


(-72x^2)+54x+(-90x)-2*108x^2=0

Wy multiply elements

(-72x^2)-216x^2+54x+(-90x)=0

We get rid of parentheses

-72x^2-216x^2+54x-90x=0

We add all the numbers together, and all the variables

-288x^2-36x=0

a = -288; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·(-288)·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*-288}=\frac{0}{-576}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*-288}=\frac{72}{-576}
=-1/8
$