When 20 is subtracted from the square of a certain number, the result is 8 times that number. Find the number

Let's denote the number we're looking for as x.

The problem can be translated into the following equation: x^2 - 20 = 8x.

To solve for x, we first rearrange the equation to set it equal to zero: x^2 - 8x - 20 = 0.

This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = -8, and c = -20.

We can solve this equation using the quadratic formula, which is x = [-b ± sqrt(b^2 - 4ac)] / (2a).

Substituting the values of a, b, and c into the formula, we get x = [8 ± sqrt((-8)^2 - 41(-20))] / (2*1) = [8 ± sqrt(64 + 80)] / 2 = [8 ± sqrt(144)] / 2 = [8 ± 12] / 2.

So the solutions are x = (8 + 12) / 2 = 10 and x = (8 - 12) / 2 = -2.

Therefore, the number we're looking for could be either 10 or -2.