Apositive integer is 47 more than 9 times another. their product is 18601860. find the two integers.

Y = 9x + 47
and 
xy = 18601860

substitute for y in second equation:-

x(9x + 47) = 18601860

9x^2 + 47x - 18601860  = 0

factoring 18601860  is  a pain so we use the quadratic  formula:-

x =   [(-47 +/- sqrt (47^2 - 4*9*-18601860)]  /  18

this gives x = 1435 , -1440   so we want x=1435 as its positive

this make y = 9(1435) + 47  =  12962

the 2 integers are 1435 and 12962