To solve the equation
\[ 811(x + 45) = 2455, \]
we first divide both sides by 811 to isolate the term with \( x \):
\[ x + 45 = \frac{2455}{811}. \]
Next, we need to calculate \( \frac{2455}{811} \):
\[ \frac{2455}{811} \approx 3.029. \]
Now, we can continue with the equation:
\[ x + 45 \approx 3.029. \]
Next, we subtract 45 from both sides:
\[ x \approx 3.029 - 45. \]
Finally, calculating the right side:
\[ x \approx -41.971. \]
Thus, the solution is approximately:
\[ x \approx -41.971. \]