I am planning to apply to a Chemistry graduate program and I am interested in both drug delivery and computational chemistry fields, which are not quite related to each other. I have backgrounds in both of those fields. If I state both of them in my statement of purpose would it have a positive or negative effect? Would the admission committee see me as a versatile researcher, or would it see me as someone who doesn't know what he wants to do?
I assume that you are talking about a Ph.D. program rather than a Masters (which are typically rather shorter and more focused). Beginning Ph.D. students are not generally expected to have a well-developed research agenda. Learning how to focus and formulate a good research agenda is an important part of what you learn in the process of getting your Ph.D., and it is generally understood that your focus and area may shift along the way.
What the professors considering your application are more likely to be interested in is whether you are thinking clearly and carefully about what you are interested in and why. If you are sincerely interested in both areas, then explain clearly why each one interests you and how you see your background as supporting that interest. Make sure to say that you could see yourself focusing on either one, depending on the program and professors that you work with. This will give the committee clear evidence that you aren't just non-committal, while at the same time avoiding artificially restricting your possible matches.