Just use solve. Or vpasolve will also suffice, since this is a polynomial, vpasolve will give all solutions.
lamb = solve(f_lambda1,'maxdegree',4)
Of course, that produces a lengthy, unreadable mess. If you want "the" lambda value, then use vpa on that.
vpa(lamb)
ans =
- 0.00011080430165098438873831754345607 + 0.000010811919008810757147508304534553i
- 0.00011080430165098438873831754345607 - 0.000010811919008810757147508304534553i
0.0023313621528906538102259208492412 + 0.0000055949768600504265689959078403377i
0.0023313621528906538102259208492412 - 0.0000055949768600504265689959078403377i
Where we see 4 solutions and only 4. Since your problem is a quartic polynomial in lambda1, those are all the solutions. I have no idea which one you think is correct.
