Algebraic Manipulation !

Geometry Level 5

Let xR+x\in \mathbb{R}^{ + } and f(x)=576+x224x+49+x273xf\left( x \right) = \sqrt { 576+{ x }^{ 2 }-24x } +\sqrt { 49+{ x }^{ 2 }-7\sqrt { 3 } x } .

If we set xx positive variable in such a way that f(x)f\left( x \right) is Minimum possible, then for this condition, find the value of E=336243x7x4.E\quad =\quad \frac { 336-24\sqrt { 3 } x -7x }{ 4 } .

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