Answer
$x=\left\{
-\dfrac{5}{7},1
\right\}$
Work Step by Step
Using $ax^2+bx+c=0,$ the given equation,
\begin{align*}\require{cancel}
7x^2-2x-5=0
,\end{align*}
the values of $a,b, \text{ and }c $ are $a=
7
,$ $b=
-2
,$ and $c=
-5
.$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}
x&=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(7)(-5)}}{2(7)}
\\\\&=
\dfrac{2\pm\sqrt{4+140}}{14}
\\\\&=
\dfrac{2\pm\sqrt{144}}{14}
\\\\&=
\dfrac{2\pm\sqrt{12^2}}{14}
\\\\&=
\dfrac{2\pm12}{14}
\end{align*}
\begin{array}{lcl}
\dfrac{2-12}{14} &\text{ OR }& \dfrac{2+12}{14}
\\\\
=\dfrac{-10}{14} && =\dfrac{14}{14}
\\\\
=-\dfrac{5}{7} && =1
\end{array}
The solutions are $
x=\left\{
-\dfrac{5}{7},1
\right\}
.$
