5/(6x)-1/12=8/(3x)

Solution for 5/(6x)-1/12=8/(3x) equation:

5/(6x)-1/12=8/(3x)

We move all terms to the left:

5/(6x)-1/12-(8/(3x))=0


Domain of the equation: 6x!=0

x!=0/6

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

5/6x-(+8/3x)-1/12=0

We get rid of parentheses

5/6x-8/3x-1/12=0

We calculate fractions


(-54x^2)/216x^2+180x/216x^2+(-576x)/216x^2=0

We multiply all the terms by the denominator


(-54x^2)+180x+(-576x)=0

We get rid of parentheses

-54x^2+180x-576x=0

We add all the numbers together, and all the variables

-54x^2-396x=0

a = -54; b = -396; c = 0;
Δ = b2-4ac
Δ = -3962-4·(-54)·0
Δ = 156816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{156816}=396$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-396)-396}{2*-54}=\frac{0}{-108}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-396)+396}{2*-54}=\frac{792}{-108}
=-7+1/3
$