Question

A book is opened, and the PRODUCT of the two visible page numbers is found to be 306.

Answer 1

X(x+1) = 306

Distribute the x

x² + x = 306

move all terms to the left and set the equal to zero (be sure to change the sign for all terms moved)

x² + x - 306 = 0
x         -17
x           18

(x - 17)(x + 18)

x =  -18, 17

pg. 17 & 18 is visible

hope this helps

Answer 2

To solve this, first note that the page numbers you open up to would be consecutive numbers. Knowing this, you can use variables to represent each page number. The first page number can be represented by x and the page following it can be represented by x+1. Then, since the product of the page numbers is 306, you can show this by using this equation:
x(x+1)=306

When you simplify the equation, you get x^2+x=360.

Then, subtract 360 from both sides to set the expression to 0, which is important since you can use the expression to solve for x. This would result in x^2+x-360=0

To solve for x, factor the expression (to factor, find two numbers that multiply up to -306 and add up to 1). When you factor, you should get (x-17)(x+18)=0.

Then, set each factor equal to 0 to solve for x. This would look like this:
(x-17)=0
(x+18)=0

When you solve for x, you get x=-18 and x=17. However, since x represents the number of pages, it cannot be a negative number, therefore one of the x values cannot be -18. This leaves x=17 as one of your page numbers. Then, since the following page number is represented as x+1, the page after 17 would be 18. 

Your answers to this problem would be that the page numbers the book opened up to are pages 17 and 18.