1/3x-1/2x-5/6=1/12

Solution for 1/3x-1/2x-5/6=1/12 equation:

1/3x-1/2x-5/6=1/12

We move all terms to the left:

1/3x-1/2x-5/6-(1/12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-1/2x-5/6-(+1/12)=0

We get rid of parentheses

1/3x-1/2x-5/6-1/12=0

We calculate fractions


(-720x^2)/2592x^2+(-72x^2)/2592x^2+864x/2592x^2+(-1296x)/2592x^2=0

We multiply all the terms by the denominator


(-720x^2)+(-72x^2)+864x+(-1296x)=0

We get rid of parentheses

-720x^2-72x^2+864x-1296x=0

We add all the numbers together, and all the variables

-792x^2-432x=0

a = -792; b = -432; c = 0;
Δ = b2-4ac
Δ = -4322-4·(-792)·0
Δ = 186624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{186624}=432$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-432)-432}{2*-792}=\frac{0}{-1584}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-432)+432}{2*-792}=\frac{864}{-1584}
=-6/11
$