How to compute Hesse normal form of plane equation?

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I was studying this answer but it doesn't provide me with what I need.

Say I give you this plane's equation:

$x + y - z + 2 = 0$

Is my goal to obtain $-1$ instead of the $2$? I usuall see square roots in Hesse normal form, so I believe you multiply a vector by its length?

Can someone guide me through this calculation, step-by-step?