3/x=6/3x-4

Solution for 3/x=6/3x-4 equation:

3/x=6/3x-4

We move all terms to the left:

3/x-(6/3x-4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

3/x-6/3x+4=0

We calculate fractions


9x/3x^2+(-6x)/3x^2+4=0

We multiply all the terms by the denominator


9x+(-6x)+4*3x^2=0

Wy multiply elements

12x^2+9x+(-6x)=0

We get rid of parentheses

12x^2+9x-6x=0

We add all the numbers together, and all the variables

12x^2+3x=0

a = 12; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·12·0
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*12}=\frac{-6}{24}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*12}=\frac{0}{24}
=0
$