Finding the $x$ and $y$ part of the side of the triangle I need help finding x and y in this triangle. 
Conditions:
It is not a right triangle;
there are no given angles;
$u$ doesn't bisect the corresponding angle;
$u$ doesn't split $c$ in two equal parts;
$c,b,a$ and $u$ are given;
Triangle example


Check someone did suggest Stewart's Theorem as a comment!
$xb^2 + yc^2 = (x+y)(u^2+xy)=au^2+axy$
From here, $x$ can be found out this way:
\begin{align}
& x(b^2-ay)+yc^2=au^2 \\
& \implies x(b^2-ay-c^2)=a(u^2-c^2) \\
& \implies \boxed{x = \frac{a(u^2-c^2)}{b^2-ay-c^2}}
\end{align}
Similarly, $$\boxed{y=a-x =a- \frac{a(u^2-c^2)}{b^2-ay-c^2}}$$
