The first sentence is not grammatically correct. If you want to use the conditional, you have to use one of the conditional tenses.
Your second sentence is fine. Here, "would" implies the condition of "being able to persuade the tutor". I don't think there is much of a difference in grammar between the structures "If A had (done) B" and "Had A (done) B":
If you had bought the stock back then, you would be rich today.
Had you bought the stock back then, you would be rich today.
so if you are confused about how to start the conditional with "had" just write it starting with "if" and then convert:
If you had got better grades, you would be making more money now.
Had you got better grades, you would be making more money now.
Your example is a little unclear to me because, presumably, you still have time to read Betty Azar if you want to persuade your tutor in the future.
If you read Betty Azar carefully, you will be able to persuade your tutor.
If your chance has already passed, then you should change to the past tense to indicate a missed opportunity:
Had you read Betty Azar carefully, you would have been able to persuade your tutor.