180=(2n)(n-1)

Solution for 180=(2n)(n-1) equation:

180=(2n)(n-1)

We move all terms to the left:

180-((2n)(n-1))=0


We calculate terms in parentheses: -(2n(n-1)), so:

2n(n-1)

We multiply parentheses

2n^2-2n

Back to the equation:

-(2n^2-2n)


We get rid of parentheses

-2n^2+2n+180=0

a = -2; b = 2; c = +180;
Δ = b2-4ac
Δ = 22-4·(-2)·180
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-38}{2*-2}=\frac{-40}{-4}
=+10
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+38}{2*-2}=\frac{36}{-4}
=-9
$