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

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

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

We move all terms to the left:

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

We calculate fractions


48x^2/144x^2+48x/144x^2+(-36x)/144x^2-3=0

We multiply all the terms by the denominator


48x^2+48x+(-36x)-3*144x^2=0

Wy multiply elements

48x^2-432x^2+48x+(-36x)=0

We get rid of parentheses

48x^2-432x^2+48x-36x=0

We add all the numbers together, and all the variables

-384x^2+12x=0

a = -384; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-384)·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*-384}=\frac{-24}{-768}
=1/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-384}=\frac{0}{-768}
=0
$