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

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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 $

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