Let $f:\mathbb{R} \to \mathbb{R}$ be a twice differentiable function with $f''(x)>0$. Solve the following equation in $\mathbb{R}$: $$f(2x+4)-f(2x+1)=f(x+3)-f(x+1).$$
I am stuck in this problem.
I sense that the mean value theorem could be useful. I used $f(x)=x^2$ to see if it gives a nice solution (like $0$) but it gives that the only solution is $-\dfrac{7}{8}$.
Any help will be appreciated.