Delta and factorization of polynomials?

I am wondering if Delta (b square minus 4ac) has any relation or can determine if a quadratic polynomial (with a degree of 2) can be factorized?

To put it simply, let say, a quadratic expression 30x^2 + 37x + 84 , it can either be factorized into (x-a)(x-b) where a and b are nice integers by cross method or cannot be factorized into integral a and b. So besides trial and error test with cross method, is there any quick way or using delta can determine whether it can be factorized into integral a and b in form of (x-a)(x-b)?

thanks all