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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

6x/3x^2+(-1x)/3x^2-5=0

We multiply all the terms by the denominator


6x+(-1x)-5*3x^2=0

Wy multiply elements

-15x^2+6x+(-1x)=0

We get rid of parentheses

-15x^2+6x-1x=0

We add all the numbers together, and all the variables

-15x^2+5x=0

a = -15; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-15)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-15}=\frac{-10}{-30}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-15}=\frac{0}{-30}
=0
$