Answer
$\textbf{(a)}\hspace{0.7cm}{x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}$
$\textbf{(b)}\hspace{0.7cm} a=\frac{1}{2}, b=-1$, and $c=-4$
$x=4\hspace{0.3cm}or \hspace{0.3cm}x=-2$
Work Step by Step
$\textbf{(a)}\hspace{0.7cm}\text{State the Quadratic Formula:}\hspace{0.3cm} \underline{x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}$
$\textbf{(b)}\hspace{0.7cm}\text{In the equation$\frac{1}{2}x^2-x-4=0\hspace{0.3cm}a=\frac{1}{2}, b=-1$, and $c=-4$. }$
$\text{So the solution of the equation is}$
$x=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(0.5)(-4)}}{2(0.5)}$
$\Rightarrow x=\dfrac{1\pm\sqrt{1+8}}{1}$
$\Rightarrow x=1\pm\sqrt{9}$
$\Rightarrow x=1\pm3\Rightarrow x=4\hspace{0.3cm}or \hspace{0.3cm}x=-2$
