Answer
$-1.379, \ or, \ -0.121$
Work Step by Step
For the equation $6x^2 +9x +1= 0$, we use the quadratic formula as follows
$$
x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a},
\\
a=6, \quad b=9, \quad c=1
.$$
That is, $$ x=\frac{-9\pm \sqrt{81-24}}{2(6) }=-1.379, \ or, \ -0.121
.$$
