x^4 = (x-20)^2

Take the square root of both sides: x^2 = ±(x-20). Case 1: x^2 = x-20 => x^2 - x + 20 = 0. The discriminant is (-1)^2 - 4(1)(20) = 1 - 80 = -79, so no real solutions. Case 2: x^2 = -(x-20) => x^2 = -x + 20 => x^2 + x - 20 = 0. Factoring gives (x+5)(x-4) = 0. The solutions are x=-5 and x=4.