3rd order equations

*Maybe somebody can help.

I have tried to solve the following rather simple equation using maxima:

(%i1) Eq: -2*q^3+3*q-1.357008100494576;
(%o1)                  - 2 q  + 3 q - 1.357008100494576

(%i2) solve(Eq,q);

rat: replaced -1.35700810049458 by -168062898/123848117 = -1.35700810049458
               sqrt(3) %i   1   sqrt(1215787242366487) %i   84031449  1/3
(%o2) [q = (- ---------- - -) (------------------------- - ---------)
                   2        2                   3/2         247696234
                                     123848117 2
                   sqrt(3) %i   1
                   ---------- - -
                       2        2
  + --------------------------------------------,
       sqrt(1215787242366487) %i   84031449  1/3
    2 (------------------------- - ---------)
                       3/2         247696234
            123848117 2
      sqrt(3) %i   1   sqrt(1215787242366487) %i   84031449  1/3
q = (---------- - -) (------------------------- - ---------)
          2        2                   3/2         247696234
                            123848117 2
                    sqrt(3) %i   1
                  - ---------- - -
                        2        2
  + --------------------------------------------,
       sqrt(1215787242366487) %i   84031449  1/3
    2 (------------------------- - ---------)
                       3/2         247696234
            123848117 2
      sqrt(1215787242366487) %i   84031449  1/3
q = (------------------------- - ---------)
                      3/2         247696234
           123848117 2realpart(%);

                         1
  + --------------------------------------------]
       sqrt(1215787242366487) %i   84031449  1/3
    2 (------------------------- - ---------)
                       3/2         247696234

            123848117 2

**A plot of Eq shows that there is at least one real root at
about -1.40.  Therefore the above result bothers me.  I have
tried a bunch of functions to get at least one of the roots
to be real, but haven't succeeded.  On the other hand, the
following
**
realpart(%);
float(%);
**[q = .5875718061709099, q = - 1.40781890504042, q = 0.82024709886951]

**agrees with MuPAD*
*
{-1.407818905, 0.5875718062, 0.8202470989}

**What am I doing wrong?

Best regards,

Esben Byskov*

-- 
Esben Byskov, Ph.D., Dr.Techn.
Professor Emeritus of Structural Analysis
Department of Civil Engineering
Aalborg University
Sohngaardsholmsvej 57
DK-9000 Aalborg
Denmark

Phone:   +45 3963 7328
          +45 2178 8365
e-mail:  eb at civil.aau.dk
          esben at annegrete.dk