1. **State the problem:** Solve the equation $$y - 2 = \frac{y^2}{9}$$ for $y$. 2. **Rewrite the equation:** Multiply both sides by 9 to eliminate the denominator: $$9(y - 2) = y^2$$ 3. **Distribute 9 on the left side:** $$9y - 18 = y^2$$ 4. **Rearrange to standard quadratic form:** $$y^2 - 9y + 18 = 0$$ 5. **Factor the quadratic:** $$y^2 - 9y + 18 = (y - 6)(y - 3) = 0$$ 6. **Set each factor equal to zero and solve:** $$y - 6 = 0 \implies y = 6$$ $$y - 3 = 0 \implies y = 3$$ 7. **Final answer:** The solutions are $$y = 6$$ and $$y = 3$$.