how to solve for M...?
i take approximation for M=1.33, am i right?
There are many numerical methods you can use for finding approximations to the real root of the equation. Use the intermediate-value theorem to narrow it down first; in this case, the real root is between and Then you can apply, for example, Newton’s method to the polynomial.
For an analytic solution, you can use Cardano’s method, which in this case yields an exact solution of for the real root (which is approximately