(n/3)-(5n/6)=(1/3)

Solution for (n/3)-(5n/6)=(1/3) equation:

(n/3)-(5n/6)=(1/3)

We move all terms to the left:

(n/3)-(5n/6)-((1/3))=0

We add all the numbers together, and all the variables

(+n/3)-(+5n/6)-((+1/3))=0

We get rid of parentheses

n/3-5n/6-((+1/3))=0

We calculate fractions


(-135n^2)/()+6n/()+()/()=0

We add all the numbers together, and all the variables

(-135n^2)/()+6n/()+1=0

We multiply all the terms by the denominator


(-135n^2)+6n+1*()=0

We add all the numbers together, and all the variables

(-135n^2)+6n=0

We get rid of parentheses

-135n^2+6n=0

a = -135; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-135)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-135}=\frac{-12}{-270}
=2/45
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-135}=\frac{0}{-270}
=0
$