Πολυώροφη εξίσωση

Να λυθεί η εξίσωση

 ${\displaystyle \frac{1}{{\displaystyle \frac{1}{{\displaystyle \frac{1}{{\displaystyle \frac{1}{x}}+{\displaystyle \frac{1}{2}}}}+{\displaystyle \frac{1}{{\displaystyle \frac{1}{x}}+{\displaystyle \frac{1}{2}}}}}}+{\displaystyle \frac{1}{{\displaystyle \frac{1}{{\displaystyle \frac{1}{x}}+{\displaystyle \frac{1}{2}}}}+{\displaystyle \frac{1}{{\displaystyle \frac{1}{x}}+{\displaystyle \frac{1}{2}}}}}}}}={\displaystyle \frac{x}{36}}$