1/3x-1/4x+1/12=2

Solution for 1/3x-1/4x+1/12=2 equation:

1/3x-1/4x+1/12=2

We move all terms to the left:

1/3x-1/4x+1/12-(2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


determiningTheFunctionDomain
1/3x-1/4x-2+1/12=0

We calculate fractions


48x^2/144x^2+48x/144x^2+(-36x)/144x^2-2=0

We multiply all the terms by the denominator


48x^2+48x+(-36x)-2*144x^2=0

Wy multiply elements

48x^2-288x^2+48x+(-36x)=0

We get rid of parentheses

48x^2-288x^2+48x-36x=0

We add all the numbers together, and all the variables

-240x^2+12x=0

a = -240; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-240)·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*-240}=\frac{-24}{-480}
=1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-240}=\frac{0}{-480}
=0
$