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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-18x^2)/216x^2+108x/216x^2+(-72x)/216x^2=0

We multiply all the terms by the denominator


(-18x^2)+108x+(-72x)=0

We get rid of parentheses

-18x^2+108x-72x=0

We add all the numbers together, and all the variables

-18x^2+36x=0

a = -18; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-18)·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*-18}=\frac{-72}{-36}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-18}=\frac{0}{-36}
=0
$