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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


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


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

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

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

A^2+A*6+4

Wy multiply elements

A^2+6A+4

Back to the equation:

-(A^2+6A+4)


We get rid of parentheses

-A^2-6A-4=0

We add all the numbers together, and all the variables

-1A^2-6A-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:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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