Floor + Factorial = ?

Algebra Level 3

x1!+x2!+x3!=224\left\lfloor \frac { x }{ 1! } \right\rfloor +\left\lfloor \frac { x }{ 2! } \right\rfloor +\left\lfloor \frac { x }{ 3! } \right\rfloor =224

Find the integer value of xx that satisfies the equation above.

Note: x\lfloor x \rfloor denotes the greatest integer that is smaller than or equal to xx.

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