I have the following system of quadratic equations:
\begin{align*} v_2x_1^2 + v_2x_1 - v_1x_2^2 - v_1x_2 & = 0\\ v_3x_1^2 + v_3x_1 - v_1x_3^2 - v_1x_3 & = 0\\ v_3x_2^2 + v_3x_2 - v_2x_3^2 - v_2x_3 & = 0 \end{align*}
How can I solve them for $x_1$, $x_2$, and $x_3$ in terms of $v_1$, $v_2$, and $v_3$ only?