(3/2x)-(2/3x)=2

Solution for (3/2x)-(2/3x)=2 equation:

(3/2x)-(2/3x)=2

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3/2x-2/3x-2=0

We calculate fractions


9x/6x^2+(-4x)/6x^2-2=0

We multiply all the terms by the denominator


9x+(-4x)-2*6x^2=0

Wy multiply elements

-12x^2+9x+(-4x)=0

We get rid of parentheses

-12x^2+9x-4x=0

We add all the numbers together, and all the variables

-12x^2+5x=0

a = -12; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-12)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-12}=\frac{-10}{-24}
=5/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-12}=\frac{0}{-24}
=0
$