360 / n + 180 * (n - 2) = 2005

360 / n + 180 * (n - 2) = 2005

360 + 180 * (n - 2) n = 2005 n
360 + 180 n ^ 2 - 360 n = 2005 n
180 n ^ 2 - 2365 n + 360 = 0
n = 473 / 72 ± 1 / 72 * √ 2133361