Answer
$x=\displaystyle \frac{-5\pm\sqrt{37}}{6}$
Work Step by Step
$ 3x^{2}+5x=1\qquad$... add $-1$ to both sides.
$ 3x^{2}+5x-1=0\qquad$... solve with the Quadratic formula.
$x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
$x=\displaystyle \frac{-5\pm\sqrt{25+12}}{6}$
$x=\displaystyle \frac{-5\pm\sqrt{37}}{6}$
