Answer
$x=\dfrac{1-\sqrt{337}}{14}\approx -1.24
\text{ and }
x=\dfrac{1+\sqrt{337}}{14}\approx 1.38$
Work Step by Step
In the given equation,
\begin{align*}
7x^2-x-12=0
,\end{align*} $a=
7
,$ $b=
-1
,$ and $c=
-12
.$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}\require{cancel}x&=
\dfrac{-(-1)\pm\sqrt{(-1)^2-4(7)(-12)}}{2(7)}
\\\\&=
\dfrac{1\pm\sqrt{1+336}}{14}
\\\\&=
\dfrac{1\pm\sqrt{337}}{14}
.\end{align*}
Hence, the solutions are $
x=\dfrac{1-\sqrt{337}}{14}\approx -1.24
\text{ and }
x=\dfrac{1+\sqrt{337}}{14}\approx 1.38
.$
