Given a system of two bivariate quadratic polynomials:
\begin{eqnarray} a_0 + a_1 x + a_2 y + a_3 xy+a_4 x^2 + a_5 y^2 &= 0 \\ b_0 + b_1 x + b_2 y + b_3 xy+b_4 x^2 + b_5 y^2 &= 0 \end{eqnarray}
is there a closed-form formula for finding all of its roots?
I'm asking becase according to Bézout's theorem there are 4 solutions and there is a closed-form formula for quartic polynomial.