2/3x+5=4/x

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

2/3x+5=4/x

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

15x^2+2x+(-12x)=0

We get rid of parentheses

15x^2+2x-12x=0

We add all the numbers together, and all the variables

15x^2-10x=0

a = 15; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·15·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*15}=\frac{0}{30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*15}=\frac{20}{30}
=2/3
$