# Thread: the roots of any algebraic equations

1. ## the roots of any algebraic equations

how do I find the roots of this equation using only pencil paper and some sort of advanced algorithm: (2+i)*x^9-2*x^5+i*x^3+6*i*x-(8-3*i)=0?

can anyone please direct me to or give me the algorithm or algorithms.

2. In general, you don't. It can be shown that there exist equations of degree higher than four whose solutions simply cannot be written in terms of algebraic operations (adding, multiplying, roots).