Question:

Sketch the root locus for the open loop transfer function of a unity feedback control sytem given below and determine the value of K for \$\xi=0.5\$

\$G(s)=\frac{K}{s(s+1)(s+3)}\$

I have drawn the root locus diagram like this

Now i tried all possible way to get the intersection point of rootlocus diagram with the 60 degree line.If i get that point i can easily find the value of K for \$\xi=0.5\$.

Is is possible to find that point without any software?