Conplete the square: 6x squared plus 13x plus 6=0

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