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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 12x-4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


12x/36x^2+(-3x)/36x^2+4+1=0

We add all the numbers together, and all the variables

12x/36x^2+(-3x)/36x^2+5=0

We multiply all the terms by the denominator


12x+(-3x)+5*36x^2=0

Wy multiply elements

180x^2+12x+(-3x)=0

We get rid of parentheses

180x^2+12x-3x=0

We add all the numbers together, and all the variables

180x^2+9x=0

a = 180; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·180·0
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*180}=\frac{-18}{360}
=-1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*180}=\frac{0}{360}
=0
$