If x^{2}-20=\sqrt{20+\sqrt{20+\sqrt{20+\sqrt{20+...\text{infinite terms}}}}}, then what is x equal to?

Explanation

Let y = \sqrt{20+\sqrt{20+...}}. Squaring both sides gives y^2 = 20 + y, which simplifies to y^2 - y - 20 = 0. Solving yields y = 5. Thus, x^2 - 20 = 5 \implies x^2 = 25 \implies x = 5.

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