  In the framework free triaxiality model branching ratio reduced
E2-transitions probabilities are studied for the full region changes of the
triaxiality parameter. The variables of quadrupole deformations $\beta_2$ and
$\gamma$ are dynamic. The Davidson potential for $\beta_2$ and $\gamma$
variables was being used. In the free triaxiality model the energy levels was
being obtained by taking into account the high-order terms of the rotational
energy operator series, which leads energy levels of ground-state-band,
$\beta$- and $\gamma$-bands to improve considerably the agreement of the
results with experimental data. The quadrupole moment of the nucleus expressed
in terms of two internal quadrupole moments: $Q_0$ is quadrupole moment about
the symmetry axis, $Q_2$ is the measure of the shape asymmetry about the
symmetry axis. The intra/inter-band reduced E2-transition probabilities
ground-state-band, $\beta$- and $\gamma$-bands are being presented and are
being expressed in terms of four parameters: $\mu_{\beta_2}$, $\mu_\gamma$,
$\gamma_0$ and $Q_0$. The influence of $\gamma$-oscillations to the reduced
probabilities of E2-transitions takes into account are numerically. The
sensitivity of the intra-/inter-band reduced E2-transition probabilities to the
triaxiality parameter was analyzed.
