series expansion

Question

I have a fourth order equation

equation (22)

and I must solve it with respect to delta0 (i.e.: Solve[equation,delta0]) to have a solution for small value of mu1 and mu2. So is it possible to expand in series of delta0 (second order) and take only first order terms in mu (i.e.: not mu1*mu2 but only mu1+mu2 ).

The equation is (23).

Could someone please help me?

Edit

Solve[Subscript[[Mu], 1]*Subscript[[Mu], 2]^2 (1+d/2-d^2/8)^4+2Subscript[[Mu], 1]^2 
      Subscript[[Mu], 2] (1+d/2-d^2/8)^3+(1+d/2-d^2/8)^2 
      (Subscript[[Mu], 1]^3+Subscript[[Mu], 2]^2-(Subscript[[Mu], 1]+
       Subscript[[Mu], 2])^3-3^(4/3) Subscript[[Mu], 1]*Subscript[[Mu], 2] 
      (Subscript[[Mu], 1]+Subscript[[Mu], 2])^(5/3))+2Subscript[[Mu],1]*
       Subscript[[Mu], 2]^2 (1+d/2-d^2/8)+Subscript[[Mu], 1]^2 Subscript[[Mu], 2]==0,d] 

... so i can't match this equation witch the one i can found in the pape