If you look in Browse All Questions, sort by Most Recent, and go back about a half dozen pages, this question has several answers.
The general consensus was that for a normal size TV, it is cheaper to replace than fix. However, for a 51" you are looking at about $500-600 current replacement cost (even if you might have paid thousands for it a few years ago), so it might be worth checking out what replacement cost is - could be near the break-even point.
Check the manufacturer's website for authorized repair centers. The manufacturer may also have a flat-rate screen replacement price, but I would guess the shipping costs to and from them would make it uneconomic.
If you have a very low homeowners/renters insurance deductible, they might cover part of the cost if the crack is accidental, though you also risk having your rate increased for only a few hundred dollars of reimbursement on this claim.
If the crack was spontaneous, you might check complaints blogs on the web to see if this might be a mnaufacturing defect, in which case the manufacturer might replace it for free.