(n/2)*((4+((n-1)*6)))=660

Solution for (n/2)*((4+((n-1)*6)))=660 equation:

(n/2)((4+((n-1)*6)))=660

We move all terms to the left:

(n/2)((4+((n-1)*6)))-(660)=0


Domain of the equation: 2)((4+((n-1)*6)))!=0

n∈R


We add all the numbers together, and all the variables

(+n/2)((4+((n-1)*6)))-660=0

We multiply all the terms by the denominator


(+n-660*2)((4+((n-1)*6)))=0


We calculate terms in parentheses: +(+n-660*2)((4+((n-1)*6))), so:

+n-660*2)((4+((n-1)*6))

determiningTheFunctionDomain
n-660*2)((4+((n-1)*6))

Wy multiply elements

-7920n^2+n

Back to the equation:

+(-7920n^2+n)


We get rid of parentheses

-7920n^2+n=0

a = -7920; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-7920)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-7920}=\frac{-2}{-15840}
=1/7920
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-7920}=\frac{0}{-15840}
=0
$