Polynomial equation solving / derivation

[Tsmolianinowa]

Hi,
I'm trying to derive x from this function:
y=-0.000001136437561*x^6 + 0.000076579364931*x^5 - 0.002024774350783*x^4 + 0.026640152891775*x^3 - 0.183135915144101*x^2 + 0.635145302827425*x - 0.051985735087849
x = ?
But I really have no idea if it is possible to do this, and 'll be grateful for any help.

 

[Deleted member 4993]

Hi,
I'm trying to derive x from this function:
y=-0.000001136437561*x^6 + 0.000076579364931*x^5 - 0.002024774350783*x^4 + 0.026640152891775*x^3 - 0.183135915144101*x^2 + 0.635145302827425*x - 0.051985735087849
x = ?
But I really have no idea if it is possible to do this, and 'll be grateful for any help.

This can be "approximated" by numerical method.

Have you been taught Newton's method of approximating roots?

 

[Tsmolianinowa]

This can be "approximated" by numerical method.

Have you been taught Newton's method of approximating roots?

Yes, thank you, I'll try.

 

[HallsofIvy]

There is no formula or other method for solving a general sixth degree equation and I don't see any relationship among the coefficients that would simplify the equation. There are a number of numerical methods you can use to get approximations to any real roots. However, that equation is of even degree and has even number of "changes of sign" in the coefficients so there is no a-priori guarantee that there is a real number root.