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