Answer
$x=\left\{
-1,4
\right\}
$
Work Step by Step
Using the Distributive Property and the properties of equality, the given equation, $
x(x-3)=4
,$ is equivalent to
\begin{align*}
x^2-3x&=4
\\
x^2-3x-4&=0
.\end{align*}
Using $ax^2+bx+c=0,$ the equation above has $a=
1
,$ $b=
-3
,$ and $c=
-4
.$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}
x&=\dfrac{-(-3)\pm\sqrt{(-3)^2-4(1)(-4)}}{2(1)}
\\\\&=
\dfrac{3\pm\sqrt{9+16}}{2}
\\\\&=
\dfrac{3\pm\sqrt{25}}{2}
\\\\&=
\dfrac{3\pm5}{2}
\end{align*}
\begin{array}{lcl}
x=\dfrac{3-5}{2} &\text{ OR }& x=\dfrac{3+5}{2}
\\\\
x=\dfrac{-2}{2} && x=\dfrac{8}{2}
\\\\
x=-1 && x=4
.\end{array}
The solutions are $
x=\left\{
-1,4
\right\}
.$
