Peter opened his book and found that the product of the page numbers for two facing pages was 156. What were the page numbers?

Assuming that the numbers are right next to each other, we have

(x) * (x+1) = 156, expanding into x^2+x=156 and then x^2+x-156=0. We can then use the quadratic formula to get x = (-1+-sqrt (1+624)) / 2 = (-1+-25) / 2 = 12, - 13. - 13 wouldn't be a page number, so 12 must be one number, and 12+1 (13) is the other!