Lets say those positive consecutive integers are x,x+1,x+2 smallest to biggest respectively.
product of smallest and largest integer x(x+2)=9*(x+1)+21
x^2+2x=9x+9+21
x^2-7x-30=0
x^2-10x+3x-30=0
x(x-10)+3(x-10)
x=- 3,x=10
we will take only positive part
so x=10
other consecutive integers would be 11,12
so answer is 10,11,12