Answer
$x=\left\{
\dfrac{7-\sqrt{109}}{10},\dfrac{7+\sqrt{109}}{10}
\right\}$
Work Step by Step
Using $ax^2+bx+c=0,$ the given equation,
\begin{align*}
5x^2-7x-3=0
,\end{align*} has $a=
5
,$ $b=
-7
,$ and $c=
-3
.$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}
x&=\dfrac{-(-7)\pm\sqrt{(-7)^2-4(5)(-3)}}{2(5)}
\\\\&=
\dfrac{7\pm\sqrt{49+60}}{10}
\\\\&=
\dfrac{7\pm\sqrt{109}}{10}
.\end{align*}
The solutions are $
x=\left\{
\dfrac{7-\sqrt{109}}{10},\dfrac{7+\sqrt{109}}{10}
\right\}
.$
