12.5.1 Olympic algebra

Problem: Find the integer part of the largest value of the parameter $a$, for which the equation $$3{\log }_5\frac{x^2+ax+4}{x}+5(x^2+(a-1)a+4)=0$$ has positive roots and all these roots are integers. If the desired value doesn't exist, write the word "no" as an answer.