Find a subspace of $\mathbb R^{3}$ of maximal dimesion so $q(\vec w)\geq 0$

Question

$q:\mathbb R^{3}\to \mathbb R$ is defined by $q(x,y,z)=-6xy-8xz$.

Find a subspace $W\subseteq\mathbb R^{3}$ of maximal dimesion so $\forall\vec w\in W,q(\vec w)\geq 0$

I know that $q$ has a diagonal form $diag(4,0,-8)$, but using directly the defenition of $q$ to find a suitable basis is not the right method... what should I do?