All zeros is one solution. If you use FindRoot you can find two more fairly easily:
In[23]:= g /. \[Gamma]1 -> 0 /. \[Delta]1 -> 0 /. \[Gamma]2 -> 0
Out[23]= {0., 0., 0.}
In[24]:= FindRoot[
g == 0, {{\[Gamma]1, 0}, {\[Delta]1, 0}, {\[Gamma]2, 0}}]
Out[24]= {\[Gamma]1 -> 0., \[Delta]1 -> 0., \[Gamma]2 -> 0.}
In[25]:= FindRoot[
g == 0, {{\[Gamma]1, 1}, {\[Delta]1, 1}, {\[Gamma]2, 1}}]
Out[25]= {\[Gamma]1 -> 0.737178, \[Delta]1 -> -0.2, \[Gamma]2 ->
0.737178}
In[26]:= ans =
FindRoot[g == 0, {{\[Gamma]1, -1}, {\[Delta]1, -1}, {\[Gamma]2, -1}}]
Out[26]= {\[Gamma]1 -> -2.80644, \[Delta]1 -> -0.2, \[Gamma]2 -> \
-2.80644}
Regards,
Neil