# Analytical method for root finding

Is there an analytical method to find the roots of the following equation?

$$y = -\frac{1}{2}{x}^{2}-\cos(x)+1.1$$

I'm sorry for the trivial question, I'm new at math! :)

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A transcendental equation like that, where the independent variable is inside and outside a transcendental function, more often than not doesn't admit neat closed-form expressions for its roots. –  Guess who it is. May 13 '12 at 8:51

This equation does not admit an analytic solution, i.e., there is no formula in terms of "elementary functions" (giving the solution in terms of additions, substractions, multiplications, divisions, $n$-th roots, exponentials and logarithms).