How to solve this nice math exponential algebra problem | Olympiad Question | x=?

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[@KhanJan-th2gd]

Interesting sir, g

[@franciscook5819]

You give no way into the problem.
539=7*7*11 suggests that (x-7) might be a factor, try substituting in x=7
lhs=343 + 196 = 539 = rhs so (x-7) is a factor.
Do the algebraic long division (of the "=0" equation) =>(x-7)(x^2 +11x + 77)=0 solve the quadratic as usual