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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


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


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

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

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

A^2+A*5-7

Wy multiply elements

A^2+5A-7

Back to the equation:

-(A^2+5A-7)


We get rid of parentheses

-A^2-5A+7=0

We add all the numbers together, and all the variables

-1A^2-5A+7=0

a = -1; b = -5; c = +7;
Δ = b2-4ac
Δ = -52-4·(-1)·7
Δ = 53
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{53}}{2*-1}=\frac{5-\sqrt{53}}{-2}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{53}}{2*-1}=\frac{5+\sqrt{53}}{-2}
$