2/x+2=4/(3x)

Solution for 2/x+2=4/(3x) equation:

2/x+2=4/(3x)

We move all terms to the left:

2/x+2-(4/(3x))=0


Domain of the equation: 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

2/x-(+4/3x)+2=0

We get rid of parentheses

2/x-4/3x+2=0

We calculate fractions


6x/3x^2+(-4x)/3x^2+2=0

We multiply all the terms by the denominator


6x+(-4x)+2*3x^2=0

Wy multiply elements

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

We get rid of parentheses

6x^2+6x-4x=0

We add all the numbers together, and all the variables

6x^2+2x=0

a = 6; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·6·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*6}=\frac{-4}{12}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*6}=\frac{0}{12}
=0
$