Ok, this is waaaay off topic, but guess that's what these forums are for +_+

 

A kiss and a candy for anyone who can solve this equation (giving full detail on how he did that):

 

-4x^3+3x-1/2=0

Use Newton's method (calculus)

 

Basically get an estimate/guess of X (say .2), then keep doing the iteration below (computer recommended for sanity).

 

Xn+1 = Xn- f(Xn)/f'(Xn)

 

f(x) = -4x^3+3x-1/2

f'(x) is the derivative of f(x)

 

Successive X's will be converge to the "real" root (they get more accurate each time), so keep doing it until it's accurate enough for you.

 

Here's a short cut:

 

http://www.math.sc.edu/cgi-bin/sumcgi/Newton.pl

 

Answer: x=0.17364817766693

 

 

Edit: Here's an explanation (semi-proof) why Newton's method works. Stop reading just after equation (5), we're not really interested in the rest (and it gets ugly too).

If i posted some of my uni work could you write some technical reports for me please :D