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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x-4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

3x/3x^2+(-6x)/3x^2+8=0

We multiply all the terms by the denominator


3x+(-6x)+8*3x^2=0

Wy multiply elements

24x^2+3x+(-6x)=0

We get rid of parentheses

24x^2+3x-6x=0

We add all the numbers together, and all the variables

24x^2-3x=0

a = 24; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·24·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*24}=\frac{6}{48}
=1/8
$