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

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

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

We move all terms to the left:

2/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

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2+96x^2+48x+(-36x)=0

We get rid of parentheses

4x^2+96x^2+48x-36x=0

We add all the numbers together, and all the variables

100x^2+12x=0

a = 100; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·100·0
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*100}=\frac{-24}{200}
=-3/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*100}=\frac{0}{200}
=0
$