Ellipse

Let $P$ be the point to which origin has to be shifted by the translation of axes, so as to remove the first degree terms from the equation $3 x^2+y^2-6 x+4 y+4=0$. If the origin is shifted to $P$ by the translation of axes, then the transformed equation of $2 x^2+3 x y-5 y^2+2 x-23 y-24=0$ is