1/3x+18=1/2x

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

1/3x+18=1/2x

We move all terms to the left:

1/3x+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)+18=0

We get rid of parentheses

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

We calculate fractions


2x/6x^2+(-3x)/6x^2+18=0

We multiply all the terms by the denominator


2x+(-3x)+18*6x^2=0

Wy multiply elements

108x^2+2x+(-3x)=0

We get rid of parentheses

108x^2+2x-3x=0

We add all the numbers together, and all the variables

108x^2-1x=0

a = 108; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·108·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*108}=\frac{0}{216}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*108}=\frac{2}{216}
=1/108
$