12/6x+2=3/2x-1

Solution for 12/6x+2=3/2x-1 equation:

12/6x+2=3/2x-1

We move all terms to the left:

12/6x+2-(3/2x-1)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



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

x∈R


We get rid of parentheses

12/6x-3/2x+1+2=0

We calculate fractions


24x/12x^2+(-18x)/12x^2+1+2=0

We add all the numbers together, and all the variables

24x/12x^2+(-18x)/12x^2+3=0

We multiply all the terms by the denominator


24x+(-18x)+3*12x^2=0

Wy multiply elements

36x^2+24x+(-18x)=0

We get rid of parentheses

36x^2+24x-18x=0

We add all the numbers together, and all the variables

36x^2+6x=0

a = 36; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·36·0
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*36}=\frac{-12}{72}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*36}=\frac{0}{72}
=0
$