You meant for 20, right? (Be careful with parenthesis, you were missing a couple).

Using Law of Cosines you can also find that $$b^2 = (a + c)^2 - 4ac\cos^2\left(\frac{B}{2}\right)$$ (you will need the half angle formula for cosine). You can then combine what you got so far and this to solve for $\cos\left(\frac{B}{2}\right)$ (you should get a quadratic equation in $\cos\left(\frac{B}{2}\right)$).