Maxima sometimes needs help solving equations. Here is an example
(C1) solve(abs(x)=6,x);
(D1) [ABS(x) = 6]
Maxima wasn't able to solve this equation; we have help Maxima by squaring
(C2) solve((abs(x)=6)^2,x);
(D2) [x = - 6, x = 6]
Of course, in general squaring an equation my enlarge the solution set, so
you'll need to check each solution. Let's try your equation using
the squaring trick:
(C3) eq : 2.1237 = 12/(abs(3*w^2 - 4))$
(C5) solve(eq^2,w);
RAT replaced 4.51010169 by 33262//7375 = 4.510101694915254
[w = ...]
This time, we get four solutions; however, Maxima replaced floating point
numbers with rational approximations. The maxima switch 'keepfloat'
_should_ prevent this from happening, but it doesn't. See
http://www.math.utexas.edu/pipermail/maxima/2003/004983.html
Your only recourse is to convert the solution to a float. For your
problem, this works okay
(C6) float(%);
(D6) [w = - 1.79355472051736, w = 1.79355472051736, w = - 0.74173571359578
%I, w =0.74173571359578 %I]
For more complex problems, you may need to use float(rectfrom(%))).
Barton