The equation of the straight line bisecting the acute angle between the lines represented by the equation $7{\mathrm{x}}^2+6\mathrm{xy}-{\mathrm{y}}^2-5\mathrm{x}+3\mathrm{y}-2=0$ is

$7{\mathrm{x}}^2+6\mathrm{xy}-{\mathrm{y}}^2-5\mathrm{x}+3\mathrm{y}-2\equiv \left(7\mathrm{x}-\mathrm{y}+c_1\right)\left(\mathrm{x}+\mathrm{y}+c_2\right)$

$\iff c_1+7c_2=-5{\text{ and c}}_1-c_2=3$

$\iff c_1=2{\text{ and c}}_2=-1$

$\therefore$ The acute angle bisector of the angle between the lines is $\frac{7\mathrm{x}-\mathrm{y}+2}{5\sqrt{2}}+\frac{\mathrm{x}+\mathrm{y}-1}{\sqrt{2}}=0$

(or) $7\mathrm{x}-\mathrm{y}+2+5(\mathrm{x}+\mathrm{y}-1)=0$

i.e., $12\mathrm{x}+4\mathrm{y}-3=0$.