Equation with Three Unknowns and One Well Known

Bengt is sitting in the town square eating ice cream. He looks like he is deep in thought. Sture walks by and comes up to him.
"Hi there, Bengt! What are you thinking?" asks Sture.
"Oh, hi. Well, I was just thinking, if x^2 + y^2 + z^2 + 1 = x + (2y + √(23)z) / 3, what is then x, y and z / √(23)? All the numbers are real."
"But that's impossible to solve, isn't it? It's three unknowns but only one equation."
"I'm sure you can do it. You're good with numbers."

Is it possible to solve? What is the answer?