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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


48x^2/24x^2+4x^2/24x^2+(-36x)/24x^2+1+3=0

We add all the numbers together, and all the variables

48x^2/24x^2+4x^2/24x^2+(-36x)/24x^2+4=0

We multiply all the terms by the denominator


48x^2+4x^2+(-36x)+4*24x^2=0

We add all the numbers together, and all the variables

52x^2+(-36x)+4*24x^2=0

Wy multiply elements

52x^2+96x^2+(-36x)=0

We get rid of parentheses

52x^2+96x^2-36x=0

We add all the numbers together, and all the variables

148x^2-36x=0

a = 148; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·148·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*148}=\frac{0}{296}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*148}=\frac{72}{296}
=9/37
$