2x/(x+3)=5/x

Solution for 2x/(x+3)=5/x equation:

2x/(x+3)=5/x

We move all terms to the left:

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


Domain of the equation: (x+3)!=0

We move all terms containing x to the left, all other terms to the right

x!=-3

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

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

We get rid of parentheses

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

We calculate fractions


2x^2/(x^2+3x)+(-5x-15)/(x^2+3x)=0

We multiply all the terms by the denominator


2x^2+(-5x-15)=0

We get rid of parentheses

2x^2-5x-15=0

a = 2; b = -5; c = -15;
Δ = b2-4ac
Δ = -52-4·2·(-15)
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{145}}{2*2}=\frac{5-\sqrt{145}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{145}}{2*2}=\frac{5+\sqrt{145}}{4}
$