Answer
$\left\{\dfrac{1\pm\sqrt{13}}{6}\right\}$
Work Step by Step
Using $ax^2+bx+c=0,$ the given equation, $
3x^2-x-1=0
$, has $a=
3
,$ $b=
-1
,$ and $c=
-1
.$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}
x&=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(3)(-1)}}{2(3)}
\\\\&=
\dfrac{1\pm\sqrt{1+12}}{6}
\\\\&=
\dfrac{1\pm\sqrt{13}}{6}
.\end{align*}
Hence, the solution set of the equation $
3x^2-x-1=0
$ is $
\left\{\dfrac{1\pm\sqrt{13}}{6}\right\}
.$
