algebra 4th power weirdness problem

[sarah22]

How did he get x = 2 with this equation? 4x - x^4/8 = 6

Here's my solution:
32x - x^4 - 48
x( x^3 - 32 ) + 48 <---- Now I'm lost. Did he use this one? (a-b)(a^2+ab+b^2) . I tried it but can't think on what to extract.

http://www.wolframalpha.com/input/?i=4x-x^4%2F8%3D6

[Mark44]

First off, this is an equation: 4x - x^4/8 = 6
This is NOT an equation: 32x - x^4 - 48 -- An equation has an = sign.

The equation is 32x - x^4 - 48 = 0, or equivalently x^4 - 32x + 48 = 0.
This equation can be factored into (x - 2)(x^3 + 2x^2 + 4x -24) = 0.

[Mentallic]

"He" would have probably used the rational roots theorem first, if not given any more information.