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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-4x^2+12x=0

a = -4; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-4)·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*-4}=\frac{-24}{-8}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-4}=\frac{0}{-8}
=0
$