**Abstract:** In this work two mathematical methods that allow us to find the transformation of group coordinates for solvable Drinfeld doubles are presented. The first one is the BCH formula method. The Drinfeld double is a connected Lie group. Considering the theorem on the decomposition of solvable connected Lie groups we introduce Drinfeld double group coordinates. Considering Baker-Campbell-Hausdorff (BCH) formula as the solution of the exponential equation linking Lie groups and associated Lie algebras and supposing particular commutation relations for Lie algebra elements we derive commutation formulas for corresponding Lie group elements. Another method using the faithful representation is presented. Using both methods we find the transformation of Drinfeld double group coordinates for specific decompositions.