First add 20 to both sides, so the equation reads x^2 - 9x + 20 = 0. Since this is a quadratic, you expect to be able to factor it into (x+a)(x+b) = 0. You're trying to find a and b so that a + b = -9 and ab = 20. From looking at it and trying different numbers, you should get -4 and -5. (-4 + -5 = -9 and -4 * -5 = 20). So the factorization is (x-4)(x-5) = 0.
Now the only way for a product of two factors to equal zero is for one or both of them to be zero. That is, x-4 = 0 or x-5 = 0. If you solve these equations, you get x=4, x=5 as solutions.