What is the number of possible values of k for which the line...

As three points are collinear \Delta=\left|$\begin{array}{ccc}k & 1 & 3 \\ 1 & -2 & k+1 \\ 15 & 2 & -4\end{array}$\right|=0\begin{aligned} & \Rightarrow k(8-2(k+1))+1(15(k+1)+4)+3(2+30)=0 \\ & \Rightarrow k(6-2 k)+(15 k+19)+96=0 \\ & \Rightarrow 2 k^2-21 k-105=0\end{aligned}$$On solving, we will get two different values$ of k$.$