1/12x+6=15+1/3x

Solution for 1/12x+6=15+1/3x equation:

1/12x+6=15+1/3x

We move all terms to the left:

1/12x+6-(15+1/3x)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/12x-(1/3x+15)+6=0

We get rid of parentheses

1/12x-1/3x-15+6=0

We calculate fractions


3x/36x^2+(-12x)/36x^2-15+6=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-324x^2+3x+(-12x)=0

We get rid of parentheses

-324x^2+3x-12x=0

We add all the numbers together, and all the variables

-324x^2-9x=0

a = -324; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-324)·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*-324}=\frac{0}{-648}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-324}=\frac{18}{-648}
=-1/36
$