Write the equation of a line that contains $(0,0)$ and is the angle bisector of two lines

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Two lines are given: $3x-y-4=0$ and $2x+6y+3=0$. The problem requires to find the equation of the angle bisector which contains the point $M(0,0)$.

Here are my attempts: I first try to find the angle between the two given lines. Then I find the half of the angle. Then i use that half angle in order to find the coefficient k for the required line. But I still do not receive the correct answer.

I will appreciate any help. Thanks in advance.