Find all roots of $f(x)=231x^3+68x^2-9x-2$
I cannot use the cubic formula or Viete's theorem here because the polynomial is not monic. The only other way I can think of doing this is by the rational roots theorem. My only concern is that there are many divisors of 231, namely 231, -231, 1, -1, 3, 3, 77, -77, 11, -11, 7, -7.
Other than the rational roots theorem, is there any way to solve this? There might not be any easy methods to do so, but I am just wondering if I can save some time.