Determine if a user came is an organic or direct visit?

Determine if a user came is an organic or direct visit?

Is it possible to determine whether a user has come to your website via an
organic search or direct and is it then possible to store this in our
database?
We have a form on our website so essentially we want to find out if the
user came direct or via organic search and then pass this in with the form
to store 'organic' or 'direct' in our database for each enquiry.
E.g if user ABC came via direct and filled in the form they would be
stored in the database as name = ABC, referral = direct, enquiry = test.
If user XYZ came via organic and filled in the form they would be stored
in the database as name = XYZ, referral = organic, enquiry = test.
You get the picture :)
Hoping someone can help.
Thanks