I need to learn to find eigenvalues and vectors.

I can find the Characteristic polynomial (and if i have the eigenvalues i can find the vectors)

However i cannot get from the Characteristic polynomial to the eigenvalues

for example if i have a 3x3 matrix

(1 0 4)

(0 2 0)

(3 1 -3)

The Characteristic polynomial is x^3 - 19x + 30 = 0 (x=lambda)

I know that the eigenvalues are Real eigenvalues:

{-5, 2, 3}

and then i can work out the eigenvectors.

But how do you get from this step (x^3 - 19x + 30 = 0) to the eigenvalues.

Thankyou!