Question 599933
let's assume the integers are x, x+1 and x+2 respectively.


We are given that (x+1)(x+2) = 50 + 5x


We proceed to solve this equation as follows

    (x+1)(x+2)     = 50 + 5x
i.e. x^2 + 3x + 2  = 50 + 5x
i.e. x^2 - 2x + 48 = 0
i.e. (x - 8)(x - 6)= 0
i.e.             x = 8 or -6


Hence the required numbers are 8,9 and 10 or -6,-5 and -4 counting negative integers as well.