Solve for $w$.
\[
\frac{w-1}{10 w}-\frac{1}{8}=\frac{1}{w}
\]
If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".
Answer
\(\boxed{\text{Final Answer: } w = \frac{9}{8} - \frac{\sqrt{641}}{8}, \frac{9}{8} + \frac{\sqrt{641}}{8}}\)
Step 1 ：Given the equation \(\frac{w-1}{10 w}-\frac{1}{8}=\frac{1}{w}\), we need to solve for \(w\).
Step 2 ：First, we multiply the entire equation by \(80w\) to eliminate the fractions. This gives us the equation \(8w^2 - 8w - 10w + 10 = 80\).
Step 3 ：Simplifying the equation, we get \(w^2 - 18w + 10 = 0\).
Step 4 ：Applying the quadratic formula, we find the solutions to be \(w = \frac{9}{8} - \frac{\sqrt{641}}{8}\) and \(w = \frac{9}{8} + \frac{\sqrt{641}}{8}\).
Step 5 ：\(\boxed{\text{Final Answer: } w = \frac{9}{8} - \frac{\sqrt{641}}{8}, \frac{9}{8} + \frac{\sqrt{641}}{8}}\)
