(2x+4)/(5x)=(2)/(x)

Solution for (2x+4)/(5x)=(2)/(x) equation:

(2x+4)/(5x)=(2)/(x)

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

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

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

We get rid of parentheses

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

We calculate fractions


(2x^2+4x)/5x^2+(-10x)/5x^2=0

We multiply all the terms by the denominator


(2x^2+4x)+(-10x)=0

We get rid of parentheses

2x^2+4x-10x=0

We add all the numbers together, and all the variables

2x^2-6x=0

a = 2; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·2·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*2}=\frac{12}{4}
=3
$