2. Solve the equation $\frac{19 x-x^{2}}{x+1}\left(x+\frac{19-x}{x+1}\right)=84$. (2006, Ningbo City, Zhejiang Province Junior High School Mathematics Competition)
Prompt: Example 6. Answer: $x_{1}=3, x_{2}=4, x_{3}=6+$ $\sqrt{29}, x_{4}=6-\sqrt{29}$.