2014 AIME I Problem 6

The graphs y = 3(x-h)^2 + j and y = 2(x-h)^2 + k have y-intercepts of 2013 and 2014, respectively, and each graph has two positive integer x-intercepts. Find h.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.