4/3x-4=5/x

Solution for 4/3x-4=5/x equation:

4/3x-4=5/x

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


4x/3x^2+(-15x)/3x^2-4=0

We multiply all the terms by the denominator


4x+(-15x)-4*3x^2=0

Wy multiply elements

-12x^2+4x+(-15x)=0

We get rid of parentheses

-12x^2+4x-15x=0

We add all the numbers together, and all the variables

-12x^2-11x=0

a = -12; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-12)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-12}=\frac{22}{-24}
=-11/12
$