1/3x-1/18=1/2x

Solution for 1/3x-1/18=1/2x equation:

1/3x-1/18=1/2x

We move all terms to the left:

1/3x-1/18-(1/2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(+1/2x)-1/18=0

We get rid of parentheses

1/3x-1/2x-1/18=0

We calculate fractions


(-12x^2)/108x^2+36x/108x^2+(-54x)/108x^2=0

We multiply all the terms by the denominator


(-12x^2)+36x+(-54x)=0

We get rid of parentheses

-12x^2+36x-54x=0

We add all the numbers together, and all the variables

-12x^2-18x=0

a = -12; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-12)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-12}=\frac{36}{-24}
=-1+1/2
$