Solve x when f(x)=6?

Question

f(x)=x^3 - 4/x
f(x)=6
therefore,
6=x^3 - 4/x

What is x? I know the answer, but i dont know how to figure it out. x=2, but how do i find out that x=2 without guessing?

Additional Details:

-x^4-6x=4 still doesnt help

-replacing x with 6 does not equal 2,
(someone told me to do that when i posted this question earlier)
x=2, but how do i find out x=2, when y or f(x)=6 without graphing or guessing.

*i know for a fact x=2, i have the answers, im just curious as to how to find out the answer.

*also this isn't the entire question, it is part of finding the derivative of the inverse f of a.

Answer 1

6 = x^3 - 4/x

multiply through by x...

6x = x^4 - 4

rearrange...

x^4 - 6x - 4 = 0

Solving quintic equations is generally no fun at all. However, this one is in Bring-Jerrard form, which makes things a little easier. Hopefully that helps a little.