Minimum-variance mix of two assets

Two assets have volatilities $\sigma_1 = 20\%$ and $\sigma_2 = 30\%$ and correlation $\rho = 0.5$. You must be fully invested: $w_1 + w_2 = 1$. Use a Lagrange multiplier to find the weights that minimize portfolio variance, and give the resulting volatility. For which correlations does the minimum-variance portfolio short the second asset?