Using the fixed point method, we prove the Ulam-Hyers stability of the orthogonally additive and orthogonally quadratic functional equation $$f(frac{x}{2}+y)+f(frac{x}{2}-y)+f(frac{x}{2}+z)+f(frac{x}{2}-z)=frac{3}{2}f(x)-frac{1}{2}f(-x)+f(y)+f(-y)+f(z)+f(-z)$$ (0.1) for all $x$, $y$, $z$ with $x{ot}y$, in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.