Problem is that the i7-3610QM and i7-3840QM processors are only available in Socket G2 and FCPGA (BGA1224) packages and you probably have the latter. FCPGA chips are solder-stamped directly onto the motherboard at the factory, they aren't mounted in sockets and they can't be removed without some costly rework tools, they are only sold in roll/tape format (in quantities of 1000), and they're both functionally EOL because Intel has already moved on to newer and smaller things.
You could only upgrade an FCPGA processor by upgrading the entire motherboard. Probably only with another G55 motherboard. And I don't think Asus offered any G55 models with the i7-3840QM.
The only way to tell is physical inspection, tools like CPUID don't always report mobile form factors accurately. But if you do have a Socket G2 processor, why not go for an i7-3940XM?
Final upgrade cost would likely be more than resale-and-replace cost, especially if you have to pay for time and labour.
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