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For a positive integer $m$ and a real number $c$, let $R = R(m,c,2)$ denotethe 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 coloringof 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  $$  R(1, c, a) =  \begin{cases}  \frac{c}{a-1} & \text{if $ \left( a-1 \right) \mid c$} \newline  \infty & \text{otherwise.}  \end{cases}  $$

The Discrete Rado Number for $x_1 + x_2 + \dots + x_m + c = 2x_0$