The 2-color Rado number of $x_1+x_2+\cdots +x_n=y_1+y_2+\cdots +y_k$

In 1982, Beutelspacher and Brestovansky determined the 2-color Rado number of the equation $$x_1+x_2+\cdots +x_{m-1}=x_m$$ for all $m\ge 3.$ Here we extend their result by determining the 2-color Rado number of the equation $$x_1+x_2+\cdots +x_n=y_1+y_2+\cdots +y_k$$ for all $n\ge 2$ and $k\ge 2.$ As a consequence, we determine the 2-color Rado number of $$x_1+x_2+\cdots +x_n=a_1{y}_1+\cdots +a_{\mathrm{\ell }}{y}_{\mathrm{\ell }}$$ in all cases where $n\ge 2$ and $n\geq a_1+\cdots +a_{\ell},$andinmostcaseswhere$n\geq 2$and$2n\geq a_1+\cdots +a_{\ell}.$