1/3x-4/6=2+1/12x

Solution for 1/3x-4/6=2+1/12x equation:

1/3x-4/6=2+1/12x

We move all terms to the left:

1/3x-4/6-(2+1/12x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(1/12x+2)-4/6=0

We get rid of parentheses

1/3x-1/12x-2-4/6=0

We calculate fractions


(-144x^2)/1296x^2+432x/1296x^2+(-108x)/1296x^2-2=0

We multiply all the terms by the denominator


(-144x^2)+432x+(-108x)-2*1296x^2=0

Wy multiply elements

(-144x^2)-2592x^2+432x+(-108x)=0

We get rid of parentheses

-144x^2-2592x^2+432x-108x=0

We add all the numbers together, and all the variables

-2736x^2+324x=0

a = -2736; b = 324; c = 0;
Δ = b2-4ac
Δ = 3242-4·(-2736)·0
Δ = 104976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{104976}=324$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(324)-324}{2*-2736}=\frac{-648}{-5472}
=9/76
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(324)+324}{2*-2736}=\frac{0}{-5472}
=0
$