How can I solve this equation $3x^5-x^2/2+x+1=0$ Maybe I am just too tired, but I dont know how to solve this??
Can you point me in right direction. Thanks!!!
 A: There is one real root, approximately $-0.59622$; you can find it using the bisection method.  It's not "nice", unfortunately.
The bisection method:
Start with real numbers $L,R$, such that $f(L), f(R)$ are of different signs, and $L<R$.  Now,  set $T$ (for trial) to be $T=\frac{L+R}{2}$.  Evaluate $f(T)$.  If it is the same sign as $L$, then start over using $T,R$ as the new interval.  If instead $f(T)$ is the same sign as $R$, then start over using $L,T$ as the new interval.
This method cuts the interval's length in half every time, so it converges quite quickly -- one binary digit every step.
A: As said by vadim123, there is only one real root. By inspection, you can locate it between $x=-1$ and $x=0$. At this point, you can use the classical bisection method or, if you want a faster convergence, Newton method.  
Just be lazy (as I am) and start iterating at $x=-1$. The successive iterates will then be $-0.794118$, $-0.657914$, $-0.603276$, $-0.596322$, $-0.596225$ which is the solution. 
If you start iterating at $x=0$, the first iterate will be $-1.0000$ and we should be back to the previous scheme.
