4/3x-2=58/x

Solution for 4/3x-2=58/x equation:

4/3x-2=58/x

We move all terms to the left:

4/3x-2-(58/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-(+58/x)-2=0

We get rid of parentheses

4/3x-58/x-2=0

We calculate fractions


4x/3x^2+(-174x)/3x^2-2=0

We multiply all the terms by the denominator


4x+(-174x)-2*3x^2=0

Wy multiply elements

-6x^2+4x+(-174x)=0

We get rid of parentheses

-6x^2+4x-174x=0

We add all the numbers together, and all the variables

-6x^2-170x=0

a = -6; b = -170; c = 0;
Δ = b2-4ac
Δ = -1702-4·(-6)·0
Δ = 28900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28900}=170$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-170)-170}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-170)+170}{2*-6}=\frac{340}{-12}
=-28+1/3
$