Assigning admin roles:
https://support.office.com/en-us/article/Assigning-admin-roles-eac4d046-1afd-4f1a-85fc-8219c79e1504?ui=en-US&rs=en-US&ad=US

There is different ways to achieve BUs delegation:
o   Split to multiple tenants (other impacts)
o   Use a packaged third party offer (for example http://delegate365.com/)
It should also be possible to use group management provided by Azure AD (Azure AD Premium subscription required), but that need to be confirmed in term of feasibility and supportability:
Azure AD Delegated Group Management: Feature walk through
http://blogs.technet.com/b/ad/archive/2014/04/07/azure-ad-delegated-group-management-feature-walk-through.aspx

 

Please note that Azure AD Premium currently offers (in Preview)  a solution about delegation:

https://msdn.microsoft.com/en-us/library/azure/dn832057.aspx