Answer
$4.154, \ or, \ -2.487$
Work Step by Step
For the equation $3x^2 -5x-31= 0$, we use the quadratic formula as follows
$$
x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a},
\\
a=3, \quad b=-5, \quad c=-31
.$$
That is, $$ x=\frac{5\pm \sqrt{25+12(31)}}{2(3) }=4.154, \ or, \ -2.487
.$$
