Question

find the national root of x^4+3x^3+3x2-3x-4=0

Answer 1

using a graphic tool.  
see attached graphic

the solutions are
x1=-2
x2=0.811

check

for x=-2

x^4+3x^3+3x2-3x-4

(-2) ^4+3(-2) ^3+3(-2) ^2-4=16+(-24)+12-4=0   ok

For x=0.811

(0.811) ^4+3(0.811) ^3+3(0.811) ^2-4=0.4326+(1.6002)+1.9731-4=0   ok