Answer
$x=-\dfrac{1}{6}
\text{ and }
x=1
$
Work Step by Step
In the given equation,
\begin{align*}
6x^2-5x-1=0
,\end{align*} $a=
6
,$ $b=
-5
,$ and $c=
-1
.$
Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}\require{cancel}x&=
\dfrac{-(-5)\pm\sqrt{(-5)^2-4(6)(-1)}}{2(6)}
\\\\&=
\dfrac{5\pm\sqrt{25+24}}{12}
\\\\&=
\dfrac{5\pm\sqrt{49}}{12}
\\\\&=
\dfrac{5\pm7}{12}
\end{align*}
\begin{array}{lcl}
&\Rightarrow
\dfrac{5-7}{12} &\text{ OR }& \dfrac{5+7}{12}
\\\\&
=\dfrac{-2}{12} && =\dfrac{12}{12}
\\\\&
=-\dfrac{1}{6} && =1
\end{array}
Hence, the solutions are $
x=-\dfrac{1}{6}
\text{ and }
x=1
.$
