Node with two different voltages at the same time - Two branches (voltage source+resistor) in parallel - LTspice
Your equations are incorrect. If you define the current in one way, then that current needs to be negative for the other side.

$$\begin{align}
V_u &amp;= R\cdot i + V_1 \\
V_u &amp;= -R\cdot i + V_2 \\
\end{align}$$

$$\begin{align}
R\cdot i &amp;= V_u - V_1 \\
R\cdot i &amp;= V_2 - V_u
\end{align}$$

You find that

$$V_u = \frac{V_1 + V_2}{2}$$