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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-144x^2)/108x^2+54x/108x^2+(-18x)/108x^2=0

We multiply all the terms by the denominator


(-144x^2)+54x+(-18x)=0

We get rid of parentheses

-144x^2+54x-18x=0

We add all the numbers together, and all the variables

-144x^2+36x=0

a = -144; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-144)·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*-144}=\frac{-72}{-288}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-144}=\frac{0}{-288}
=0
$