Solve for x given formula for cubic interpolation

polynomials interpolation cubics

You can find an analytical formula for $x$ here: https://en.wikipedia.org/wiki/Cubic_equation#Trigonometric_and_hyperbolic_solutions (however first you have to transform your cubic equation to the standard form $x^3+Bx^2+Cx+D=0$ and further continue by substitution $y=x-\frac{B}{3}$ to get the so-called depressed form $x^3+Ex+F=0$).

Or you can find $x$ numerically, by means of the Newton's method for example, which however gives you only one of the solutions.

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