12/x-2=24/3x-1

Solution for 12/x-2=24/3x-1 equation:

12/x-2=24/3x-1

We move all terms to the left:

12/x-2-(24/3x-1)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

12/x-24/3x+1-2=0

We calculate fractions


36x/3x^2+(-24x)/3x^2+1-2=0

We add all the numbers together, and all the variables

36x/3x^2+(-24x)/3x^2-1=0

We multiply all the terms by the denominator


36x+(-24x)-1*3x^2=0

Wy multiply elements

-3x^2+36x+(-24x)=0

We get rid of parentheses

-3x^2+36x-24x=0

We add all the numbers together, and all the variables

-3x^2+12x=0

a = -3; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-3)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-3}=\frac{-24}{-6}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-3}=\frac{0}{-6}
=0
$