Answer
$x=-7
\text{ and }
x=7$
Work Step by Step
Using the properties of equality, the given equation, $
-3x^2+147=0
,$ is equivalent to
\begin{align*}
\dfrac{-3x^2+147}{-3}=\dfrac{0}{-3}
\\\\
x^2-49=0
\end{align*}
In the equation above, $a=
1
,$ $b=
0
,$ and $c=
-49
.$
Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}\require{cancel}x&=
\dfrac{-0\pm\sqrt{0^2-4(1)(-49)}}{2(1)}
\\\\&=
\dfrac{-0\pm\sqrt{0+196}}{2}
\\\\&=
\dfrac{\pm\sqrt{196}}{2}
\\\\&=
\dfrac{\pm14}{2}
\end{align*}
\begin{array}{lcl}
&\Rightarrow
\dfrac{-14}{2} &\text{ OR }& \dfrac{14}{2}
\\\\&
=-7 && =7
\end{array}
Hence, the solutions are $
x=-7
\text{ and }
x=7
.$
