lga1155 in an lga1550 socket can Work?
No. You cannot fit an LGA 1155 socket CPU into an LGA 1150 motherboard.
You'll have to find an LGA 1150 socket CPU since you've apparently already bought the board. Fortunately for you, the Haswell i7 4770 CPU line is LGA 1150 which is a smidgen better than the Ivy Bridge i7 3770 you're looking at. They're priced very similarly so you shouldn't see too much of a price delta between the two.
PCPartPicker part list / Price breakdown by merchant / Benchmarks
CPU: Intel Core i7-4770 3.4GHz Quad-Core Processor ($294.99 @ Newegg)
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-05-09 01:18 EDT-0400)
you should have gotten an i5 and a cheap motherboard and used the money on a way better graphics card like the gtx 760 or r9 270x. That gt640 isn't a good gpu at all. Return both of those and get an i5 4440 and a cheap h81 1150 socket motherboard and get a better gpu. Or the Xeon as mentioned for cpu.