Number of integers in the range of f(x),f(x) = 5/(5x^2+10x=8), x belongs to R

I believe the denominator would be
then then minimum value that the denominator can take is at x = -b/2a = -1 (here)

at x= -1 the denominatr becomes = 5-10+8 = 3
so the range of the denominator is
thus the range of f(x) is

Thus numer of integers is = 1