  For a positive integer $m$ and a real number $c$, let $R = R(m,c,2)$ denote
the discrete 2-color Rado number for the equation $x_1 + x_2 + \dots + x_m + c
= 2x_0$. In other words, $R$ is the smallest integer such that for any coloring
of the integers ${1, 2, \dots, R}$, there exist numbers $x_1, x_2, \dots, x_m,
x_0$, all with the same color, such that $x_1 + x_2 + \dots + x_m + c = 2x_0$.
In this article we show that if $m \geq 2$ and $c > 0$, then $$
\begin{array}{cc} R(m,c,2) =
  \begin{cases}
  \infty & \text{for $m$ even, $c$ odd} \newline
  \big\lceil \frac{m}{2} \big\lceil \frac{m+c}{2} \big\rceil + \frac{c}{2}
\big\rceil & \text{otherwise.} \end{cases} \end{array} $$ For real numbers $a$
and $c$, we look at the 2-color Rado number for the equation $x_1 + c = ax_0$.
We show that if $a > 1$ and $c > 0$, then the 2-color continuous Rado number is
$$
  R_\mathbb{R}(1, c, a) =
  \begin{cases}
  \infty & \text{if $a=1$ } \newline
  \frac{c}{a-1} & \text{otherwise.}
  \end{cases}
  $$
  From this, we will show that the discrete Rado number is
  $$
  R(1, c, a) =
  \begin{cases}
  \frac{c}{a-1} & \text{if $ \left( a-1 \right) \mid c$} \newline
  \infty & \text{otherwise.}
  \end{cases}
  $$
