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

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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} $

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