I found this page on the intersection of 2 lines. And I'm really surprised about going from:
$\begin{align*} x_1 + u_a (x_2 - x_1) &= x_3 + u_b (x_4 - x_3) \\\ y_1 + u_a (y_2 - y_1) &= y_3 + u_b (y_4 - y_3) \end{align*}$
to this
$\begin{align*} u_a &= \frac{(x_4 - x_3)(y_1 - y_3) - (y_4-y_3)(x_1-x_3)}{(y_4-y_3)(x_2-x_1)-(x_4-x_3)(y_2-y_1)} \\\ u_b &= \frac{(x_2-x_1)(y_1-y_3)-(y_2-y_1)(x_1-x_3)}{(y_4-y_3)(x_2-x_1)-(x_4-x_3)(y_2-y_1)} \end{align*}$
Could somebody carry it for me cause I always fail and get other final equation.