A big challenge

Calculus Level 5

2x422x242x+16+2x322x232x+9=0 \frac {2x - 4 \sqrt 2}{2 \sqrt{x^2 - 4 \sqrt 2 x + 16} } + \frac {2x - 3 \sqrt 2}{2 \sqrt{x^2 - 3\sqrt 2 x + 9} } = 0

If the real value of x\large{x} which satisfies the equation above can be expressed as abc\frac { a\sqrt { b } }{ c } , find a+b+ca+b+c.

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