Solve equation 1/x + x^3 + 5x=0

For x!=0, multiply the equation by x to get x^4+5x^2+1=0. Then substitute t=x^2 where t>=0. So the equation has a form t^2+5t+1. Then find the discriminant and two roots. One of the roots t2<0 doesn't meet the condition for t>=0 so we take t1=x^2, then we find two x roots, and have a final solution.