4/x-1+6/3x-1=13/3+1

Solution for 4/x-1+6/3x-1=13/3+1 equation:

4/x-1+6/3x-1=13/3+1

We move all terms to the left:

4/x-1+6/3x-1-(13/3+1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4/x+6/3x-2-(13/3+1)=0

We get rid of parentheses

4/x+6/3x-2-1-13/3=0

We calculate fractions


108x/27x^2+6x/27x^2+(-13x)/27x^2-2-1=0

We add all the numbers together, and all the variables

108x/27x^2+6x/27x^2+(-13x)/27x^2-3=0

We multiply all the terms by the denominator


108x+6x+(-13x)-3*27x^2=0

We add all the numbers together, and all the variables

114x+(-13x)-3*27x^2=0

Wy multiply elements

-81x^2+114x+(-13x)=0

We get rid of parentheses

-81x^2+114x-13x=0

We add all the numbers together, and all the variables

-81x^2+101x=0

a = -81; b = 101; c = 0;
Δ = b2-4ac
Δ = 1012-4·(-81)·0
Δ = 10201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10201}=101$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(101)-101}{2*-81}=\frac{-202}{-162}
=1+20/81
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(101)+101}{2*-81}=\frac{0}{-162}
=0
$