2/x+2+5/3x=4/x

Solution for 2/x+2+5/3x=4/x equation:

2/x+2+5/3x=4/x

We move all terms to the left:

2/x+2+5/3x-(4/x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/x+5/3x-(+4/x)+2=0

We get rid of parentheses

2/x+5/3x-4/x+2=0

We calculate fractions


(-12x+2)/3x^2+5x/3x^2+2=0

We multiply all the terms by the denominator


(-12x+2)+5x+2*3x^2=0

We add all the numbers together, and all the variables

5x+(-12x+2)+2*3x^2=0

Wy multiply elements

6x^2+5x+(-12x+2)=0

We get rid of parentheses

6x^2+5x-12x+2=0

We add all the numbers together, and all the variables

6x^2-7x+2=0

a = 6; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·6·2
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{-(-7)-1}{2*6}=\frac{6}{12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*6}=\frac{8}{12}
=2/3
$