5/x-1=4+2/3x

Solution for 5/x-1=4+2/3x equation:

5/x-1=4+2/3x

We move all terms to the left:

5/x-1-(4+2/3x)=0


Domain of the equation: 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-(2/3x+4)-1=0

We get rid of parentheses

5/x-2/3x-4-1=0

We calculate fractions


15x/3x^2+(-2x)/3x^2-4-1=0

We add all the numbers together, and all the variables

15x/3x^2+(-2x)/3x^2-5=0

We multiply all the terms by the denominator


15x+(-2x)-5*3x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-15x^2+13x=0

a = -15; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-15)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-15}=\frac{-26}{-30}
=13/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-15}=\frac{0}{-30}
=0
$