The formula for Z0 is an emphirical relation. Probably, the equation is fitted with the data of a number of microstrip lines. Nowdays advanced 3D codes estimate Z0 based on field calculator. 

@Anurag Misra 

Thanks for your reply.

I also have the same feeling that we have approximate it using some simulations.

I would rather suggest to use any of existing relations like in Edwards T.C.: Foundations for Microstrip Circuit Design, Wiley, New York 1980

@Adam Abramowicz

Thanks for the help.

I have one more concern-

Can you please suggest me from where I can purchase/download it?

The book can be read at:

https://books.google.pl/books?id=EDVlt8hXpzAC&pg=PA20&lpg=PA20&dq=Edwards+T.C.:+Foundations+for+Microstrip+Circuit+Design,+Wiley,+New+York+1980&source=bl&ots=HqW1PSewlv&sig=IUhom5Cv66ZL0F44hoUDE8lKS-M&hl=pl&sa=X&ei=97rCVILeC8LIPPaIgOgG&ved=0CC4Q6AEwAg#v=onepage&q=Edwards%20T.C.%3A%20Foundations%20for%20Microstrip%20Circuit%20Design%2C%20Wiley%2C%20New%20York%201980&f=false