Answer
When solving the ambiguous case using the law of cosines, the first step is to solve for the missing $side$. This will result in a $quadratic$ equation, which can be solved using the $Quadratic\, formula$.
Work Step by Step
We are given 2 sides and an angle.
Using law of cosines,
$b^{2}=c^{2}+a^{2}-2ca(cosB)$
If $b$,$a$,$B$ are known and $c$ is unknown, clearly this results in a quadratic equation, which can be solved for $c$.