To solve this quadratic equation, we can first rewrite it in standard form:

-x^2 + 20 = x

Bringing all terms to one side, we get:

x^2 + x - 20 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± √(b^2 - 4ac)) / 2a

Here, a = 1, b = 1, and c = -20. Plugging these values into the formula:

x = (-1 ± √(1^2 - 41(-20))) / 2(1)
x = (-1 ± √(1 + 80)) / 2
x = (-1 ± √81) / 2
x = (-1 ± 9) / 2

This gives us two possible values for x:

x = (-1 + 9) / 2 = 8 / 2 = 4
x = (-1 - 9) / 2 = -10 / 2 = -5

Therefore, the solutions to the equation are x = 4 and x = -5.