Answer
$x=-\dfrac{2}{3}\pm\dfrac{\sqrt{7}}{3}$
Work Step by Step
$3x^{2}+4x-1=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=3$, $b=4$ and $c=-1$.
Substitute the known values into the formula and simplify:
$x=\dfrac{-4\pm\sqrt{4^{2}-4(3)(-1)}}{2(3)}=\dfrac{-4\pm\sqrt{16+12}}{6}=...$
$...=\dfrac{-4\pm\sqrt{28}}{6}=\dfrac{-4\pm2\sqrt{7}}{6}=-\dfrac{4}{6}\pm\dfrac{2\sqrt{7}}{6}=-\dfrac{2}{3}\pm\dfrac{\sqrt{7}}{3}$
