b=0;
c=0.02;
f=u(1+c-u)^2;
g=r(1-u);
f1=D[f,u];
g1=D[g,u];
r1=r /. Solve[{f==g,f1==g1},{u,r}][[2]];
r2=r /. Solve[{f==g,f1==g1},{u,r}][[3]];
pl=Plot[{f,r1(1-u),r2(1-u)},{u,-0.2,1.2},ImageSize->{400,300}];
d1=r2/8;
d2=(r1+r2)/8;
d3=1.2*r1/4;
max=2*r1;
a1 = a /. Solve[{(1+d1/a)^2*a==max},a];
a2 = a /. Solve[{(1+d2/a)^2*a==max},a];
a3 = a /. Solve[{(1+d3/a)^2*a==max},a];
d:=d2;
k1:=-2(1+c);
k2:=(1+c)^2+(E^a+d)^2/E^a+b(E^a+d)^2/((E^a)^2);
k3:=-(E^a+d)^2/E^a;
w1[a_]:= u /. Solve[u^3 + k1 u^2 + k2 u +k3 == 0, u][[1]];
w2[a_]:= u /. Solve[u^3 + k1 u^2 + k2 u +k3 == 0, u][[2]];
w3[a_]:= u /. Solve[u^3 + k1 u^2 + k2 u +k3 == 0, u][[3]];
abb=Plot[Evaluate[{w1[a],w2[a],w3[a]}],{a,-6,-1},
   PlotPoints->2500,ImageSize->{400,300},AxesLabel->{"log a","u^*"}];