2/3x+1=5/x

Solution for 2/3x+1=5/x equation:

2/3x+1=5/x

We move all terms to the left:

2/3x+1-(5/x)=0


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

2/3x-(+5/x)+1=0

We get rid of parentheses

2/3x-5/x+1=0

We calculate fractions


2x/3x^2+(-15x)/3x^2+1=0

We multiply all the terms by the denominator


2x+(-15x)+1*3x^2=0

Wy multiply elements

3x^2+2x+(-15x)=0

We get rid of parentheses

3x^2+2x-15x=0

We add all the numbers together, and all the variables

3x^2-13x=0

a = 3; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·3·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*3}=\frac{26}{6}
=4+1/3
$