I was working on this fairly short equation. The solution gives different results in Maple 11.01 and 11.02:
> solve(0.981747e-8*RR+0.16549e-34*(1/RR^3-1/(0.50e-9+RR)^3)+(0.44e-26*(1+0.127324e10*RR))*10.000^2/RR^2 = 0., RR)
The equation has 7 solutions, of which 3 are real, one of which is for example -9.959429517E-10. The correct value is negative, however Maple 11.01 (build 296069) gives 9.959429517E-10, while Maple 11.02 gives -9.959429517E-10.
This is also the case for all 3 real solutions; the correct sign is negative, but 11.01 gives positive values. The 4 complex solutions appear to be correct for both 11.01 and 11.02. The same problem with 11.01 also occurs with fsolve.
I realize that the numerical values in the original equation have large exponents. However, the missing negative sign is not due to using too few digits in the calculation, indeed 11.01 gives a positive value 9.959... even when the Digits environment variable is set to very large values.