Answer
$\left\{\dfrac{1-\sqrt{21}}{10},\dfrac{1+\sqrt{21}}{10}\right\}$
Work Step by Step
The equation is in standard form:
$$5x^2-x-1=0.$$
To solve the equation $ax^2+bx+c=0$ we will use the quadratic formula:
$$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$$
Identify $a$, $b$, $c$:
$$\begin{align*}
a&=5\\
b&=-1\\
c&=-1.
\end{align*}$$
We solve the given equation by substituting the values of $a$, $b$, $c$ in the quadratic formula:
$$\begin{align*}
x&=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(5)(-1)}}{2(5)}\\
&=\dfrac{1\pm\sqrt{21}}{10}.
\end{align*}$$
The solution set of the equation is:
$$\left\{\dfrac{1-\sqrt{21}}{10},\dfrac{1+\sqrt{21}}{10}\right\}.$$
