The value of $\lambda (\left|\lambda \right|<1)suchthat2x^2-10xy+12y^2+5x+\lambda y-3=0$ represents a pair of lines is

$\begin{array}{l}GivenEquation2x^2-10xy+12y^2+5x+\lambda y-3=0\\ Comparingwitha{x}^2+2hxy+b{y}^2+2gx+2fy+c=0\\ a=2,h=-5,b=12,g=\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.,f=\raisebox{1ex}{$\lambda $}\!\left/ \!\raisebox{-1ex}{$2$}\right.,c=-3\\ representpairoflinethen\Delta =0\\ \Rightarrow abc+2fgh-a{f}^2-b{g}^2-c{h}^2=0\\ \Rightarrow 2\left(12\right)(-3)+2\left(\frac{\lambda }{2}\right)\left(\frac{5}{2}\right)(-5)-2{\left(\frac{\lambda }{2}\right)}^2-12{\left(\frac{5}{2}\right)}^2+3{(-5)}^2=0\\ \Rightarrow -72-\frac{50\lambda }{4}-2\left(\frac{{\lambda }^2}{4}\right)-12\left(\frac{25}{4}\right)+3\left(25\right)=0\\ \Rightarrow -288-50\lambda -2{\lambda }^2-300+300=0\\ \Rightarrow 2{\lambda }^2+50\lambda +288=0\\ \Rightarrow {\lambda }^2+25\lambda +144=0\\ \Rightarrow {\lambda }^2+16\lambda +9\lambda +144=0\\ \Rightarrow (\lambda +16)(\lambda +9)=0\\ \lambda =-9,-16\end{array}$