1/12x+9=1/3x-3

Solution for 1/12x+9=1/3x-3 equation:

1/12x+9=1/3x-3

We move all terms to the left:

1/12x+9-(1/3x-3)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 3x-3)!=0

x∈R


We get rid of parentheses

1/12x-1/3x+3+9=0

We calculate fractions


3x/36x^2+(-12x)/36x^2+3+9=0

We add all the numbers together, and all the variables

3x/36x^2+(-12x)/36x^2+12=0

We multiply all the terms by the denominator


3x+(-12x)+12*36x^2=0

Wy multiply elements

432x^2+3x+(-12x)=0

We get rid of parentheses

432x^2+3x-12x=0

We add all the numbers together, and all the variables

432x^2-9x=0

a = 432; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·432·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*432}=\frac{0}{864}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*432}=\frac{18}{864}
=1/48
$