The length of x- intercept made by pair of lines $2x^2+xy-6y^2-2x+17y-12=0is$ 

$\begin{array}{l}GivenEquation2x^2+xy-6y^2-2x+17y-12=0\\ Comparingwitha{x}^2+2hxy+b{y}^2+2gx+2fy+c=0\\ a=2,h=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.,b=-6,g=-1,f=\frac{17}{2},c=-12\\ LengthofX-\mathrm{int}ercept=\frac{2\sqrt{g^2-ac}}{\left|a\right|}\Rightarrow \frac{2\sqrt{1+25}}{2}\Rightarrow 5\\ \end{array}$