The length of the intercept on the x-axis cut by the pair of lines $2x^2+5xy+3y^2+6x+7y+1=0is$

Given Equation $2x^2+5xy+3y^2+6x+7y+1=0$

$\begin{array}{l}Comparingwitha{x}^2+2hxy+b{y}^2+2gx+2fy+c=0\\ a=2,h=\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.,b=3,g=3,f=\raisebox{1ex}{$7$}\!\left/ \!\raisebox{-1ex}{$2$}\right.,c=1\\ LengthofX-\mathrm{int}ercept=\frac{2\sqrt{g^2-ac}}{\left|a\right|}\Rightarrow \frac{2\sqrt{9-2}}{\left|2\right|}=\sqrt{7}\end{array}$