w1[c_,a_]:=u/.NSolve[ -c/a u^3 + c u^2 + (-c/a-1) u + c==0,u][[1]];
w3[c_,a_]:=u/.NSolve[ -c/a u^3 + c u^2 + (-c/a-1) u + c==0,u][[3]];
f1[c_,a_]:=If[Abs[Im[w1[c,a]]]<0.0001,Re[w1[c,a]],Re[w3[c,a]]];
f3[c_,a_]:=If[Abs[Im[w3[c,a]]]<0.0001,Re[w3[c,a]],Re[w1[c,a]]];

abb=Plot3D[f1[c,a],{c,0.4,0.65},{a,4,12},
PlotPoints->50,AxesLabel->{"c","A","x*"},ImageSize->{400,300}];