2/3x-2=3x/18x-12

Solution for 2/3x-2=3x/18x-12 equation:

2/3x-2=3x/18x-12

We move all terms to the left:

2/3x-2-(3x/18x-12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 18x-12)!=0

x∈R


We get rid of parentheses

2/3x-3x/18x+12-2=0

We calculate fractions


(-9x^2)/54x^2+36x/54x^2+12-2=0

We add all the numbers together, and all the variables

(-9x^2)/54x^2+36x/54x^2+10=0

We multiply all the terms by the denominator


(-9x^2)+36x+10*54x^2=0

Wy multiply elements

(-9x^2)+540x^2+36x=0

We get rid of parentheses

-9x^2+540x^2+36x=0

We add all the numbers together, and all the variables

531x^2+36x=0

a = 531; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·531·0
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*531}=\frac{-72}{1062}
=-4/59
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*531}=\frac{0}{1062}
=0
$