Answer
$2.52,\ or, \ -1.18$
Work Step by Step
For the equation $3x^2 -4x-9= 0$, we use the quadratic formula as follows
$$ x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}, \\
a=3, \quad b=-4, \quad c=-9.$$
That is,
$$ x=\frac{4 \pm \sqrt{16+108}}{2(3) }=2.52,\ or, \ -1.18
.$$
