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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


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


We calculate terms in parentheses: -(5+(+n^2-1*1+n*6)), so:

5+(+n^2-1*1+n*6)

determiningTheFunctionDomain
(+n^2-1*1+n*6)+5

We get rid of parentheses

n^2+n*6+5-1*1

We add all the numbers together, and all the variables

n^2+n*6+4

Wy multiply elements

n^2+6n+4

Back to the equation:

-(n^2+6n+4)


We get rid of parentheses

-n^2-6n-4=0

We add all the numbers together, and all the variables

-1n^2-6n-4=0

a = -1; b = -6; c = -4;
Δ = b2-4ac
Δ = -62-4·(-1)·(-4)
Δ = 20
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{5}}{2*-1}=\frac{6-2\sqrt{5}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{5}}{2*-1}=\frac{6+2\sqrt{5}}{-2}
$