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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


6x/2x^2+(-12x)/2x^2+1-2=0

We add all the numbers together, and all the variables

6x/2x^2+(-12x)/2x^2-1=0

We multiply all the terms by the denominator


6x+(-12x)-1*2x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2-6x=0

a = -2; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-2)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-2}=\frac{12}{-4}
=-3
$