(5/x)+(1/3x)=4x/3

Solution for (5/x)+(1/3x)=4x/3 equation:

(5/x)+(1/3x)=4x/3

We move all terms to the left:

(5/x)+(1/3x)-(4x/3)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/x)+(+1/3x)-(+4x/3)=0

We get rid of parentheses

5/x+1/3x-4x/3=0

We calculate fractions


(-4x^2)/27x^2+135x/27x^2+x/27x^2=0

We multiply all the terms by the denominator


(-4x^2)+135x+x=0

We add all the numbers together, and all the variables

(-4x^2)+136x=0

We get rid of parentheses

-4x^2+136x=0

a = -4; b = 136; c = 0;
Δ = b2-4ac
Δ = 1362-4·(-4)·0
Δ = 18496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18496}=136$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(136)-136}{2*-4}=\frac{-272}{-8}
=+34
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(136)+136}{2*-4}=\frac{0}{-8}
=0
$