(n/6)-(5n/12)=(1/6)

Solution for (n/6)-(5n/12)=(1/6) equation:

(n/6)-(5n/12)=(1/6)

We move all terms to the left:

(n/6)-(5n/12)-((1/6))=0

We add all the numbers together, and all the variables

(+n/6)-(+5n/12)-((+1/6))=0

We get rid of parentheses

n/6-5n/12-((+1/6))=0

We calculate fractions


(-1080n^2)/()+12n/()+()/()=0

We add all the numbers together, and all the variables

(-1080n^2)/()+12n/()+1=0

We multiply all the terms by the denominator


(-1080n^2)+12n+1*()=0

We add all the numbers together, and all the variables

(-1080n^2)+12n=0

We get rid of parentheses

-1080n^2+12n=0

a = -1080; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-1080)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-1080}=\frac{-24}{-2160}
=1/90
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-1080}=\frac{0}{-2160}
=0
$