4/3x=5+8/x

Solution for 4/3x=5+8/x equation:

4/3x=5+8/x

We move all terms to the left:

4/3x-(5+8/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

4/3x-(8/x+5)=0

We get rid of parentheses

4/3x-8/x-5=0

We calculate fractions


4x/3x^2+(-24x)/3x^2-5=0

We multiply all the terms by the denominator


4x+(-24x)-5*3x^2=0

Wy multiply elements

-15x^2+4x+(-24x)=0

We get rid of parentheses

-15x^2+4x-24x=0

We add all the numbers together, and all the variables

-15x^2-20x=0

a = -15; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-15)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*-15}=\frac{0}{-30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-15}=\frac{40}{-30}
=-1+1/3
$