6x^2+13x+6=0 subtract 6 from both sides
6x^2+13x=-6 divide all terms by 6
x^2+13x/6=-1 halve the linear coefficient, square it, and add it to both sides of the equation, (13/12)^2=169/144
x^2+13x/6+169/144=169/144-144/144 now the left side is a perfect square
(x+13/12)^2=25/144 take the square root of both sides
x+13/12=±5/12 subtract 13/12 to both sides
x=-13/12±5/12
x=(-13±5)/12
