show inequality by using bramble hilbert lemma

Question

Let $\mathbb{T}$ be a triangle in $\mathbb{R}^2$ with vertices $x_1,x_2,x_3$. $|\mathbb{T}|$ is the Lebesgue measure of $\mathbb{T}$. I want to show the following inequality. \begin{equation} (\forall g \in H^2(\mathbb{T})) |\int _{\mathbb{T}} g(x)dx - \frac{|\mathbb{T}|}{3}\sum _{k=1}^3 g(x_i)|\leq\delta\times |\mathbb{T}|\times |g| _{H^2(\mathbb{T})} \end{equation} for some $\delta \in ]0,+\infty[$. I would like to show this inequality by using the Bramble-Hilbert lemma. Could somebody help me with that? Thanks!