Find all pairs of positive integers $(x,y)$ : $x(x+1) = y(y+1)(y+2)$

Question

Find all pairs of positive integers $(x,y)$ : $$x(x+1) = y(y+1)(y+2)$$

I was able to find only two pairs: $(2,1)$ and $(14,5)$ and looks like no more exists. How to prove it?