If $(1,5,35),(7,5,5),(1,\lambda ,7)\text{ and }(2\lambda ,1,2)$  are coplanar, then the sum of all possible values of $\lambda$ is

The points $(1,5,35),(7,5,5),(1,\lambda ,7)\text{ and }(2\lambda ,1,2)$ are coplanar
$\begin{array}{l}\Rightarrow \left[\begin{array}{lll}\overrightarrow{AB}& \overrightarrow{AC}& \overrightarrow{AD}\end{array}\right]=0\Rightarrow \left|\begin{array}{ccc}6& 0& -30\\ 0& \lambda -5& -28\\ 2\lambda -1& -4& -33\end{array}\right|=0\\ \Rightarrow 6[-33(\lambda -5)-112]-30[-(\lambda -5\left)\right(2\lambda -1\left)\right]=0\\ \Rightarrow -33(\lambda -5)-112+5(\lambda -5)(2\lambda -1)=0\Rightarrow -33\lambda +165-112+10{\lambda }^2-55\lambda +25=0\\ \Rightarrow 10{\lambda }^2-88\lambda +78=0\Rightarrow 5{\lambda }^2-44\lambda +39=0\text{. Sum of the values of }\lambda \text{ is }44/5.\end{array}$