Two functions too trouble

Geometry Level 4

Let $$f(x) = 2(a-x)(x+\sqrt{x^{2}+9})$$ and $$g(y) = 9+7\cos ^{2} x + 24\sin x \cos x$$ be two functions having same maximum value.That is, $$f_\text{max} = g_\text{max}$$.

Given that $$a>0$$,find the value of $$a$$.

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