further calcul tell us:
1) 3a(5-b) = b, a = 2/(6-3p), b = 3+p ==> p = -1, a=2/9, b=2
2) 3a(5-b) = 2, a = 2/(6-3p), b = 3+p ==> p = -1, a=2/9, b=2
both pathes lead to your original wrong answer f(0)=8/9
this proof that you are "computer" major, just a little short in analysis and reasoning.
Mes respects monsieur!