There have been several posts on this topic on math.se, such as this one with the same title. However all the posts I found contained coefficients to $x^2$, that were perfect squares. I am looking for integer values for which $5x^2+2x+1$ is a perfect square.
EDIT: After looking at the first few solutions I have come to the conjecture that the only solutions is two consecutive fibonnaci multiples. i.e. $2=1\cdot2, 15=3\cdot5, 104=8\cdot13, 714 = 21\cdot34$