sequences and series - How to find the square root of $sqrt{20+sqrt{20+sqrt{20 + cdots}}}$

Generally, I know how to calculate the sq roots or cube roots, but I am confused in this question, don't know how to do this:

$$\sqrt{20+\sqrt{20+\sqrt{20 + \cdots}}}$$

Note: Answer given in the key book is $5$.

Not allowed to use calculator.

Answer

HINT:

Let $\displaystyle S=\sqrt{20+\sqrt{20+\sqrt{20+\cdots}}}$ which is definitely $>0$

$\displaystyle\implies S^2=20+S\iff S^2-S-20=0$

But we need to show the convergence of the sum