Question

Find an equation of the line that bisects the acute angles formed by the lines with equations 2x+y-5=0 and 3x-2y+6=0

Answer 1

The solving for the first one should be like this 

$2x+y-5/sqrt 2^2 1^2=2x+y-5/sqrt5$
And the next part $3x-2y+6/sqrt 3^2 -2^2=3x-2y+6/sqrt13$

After these manipulations just multiply them 
$(2sqrt13-3sqrt5)x+(sqrt13+2sqrt5) y-5sqrt13-6sqrt5=0$
And finally you need to square and simplify for the completed answer