Answer
$x=0
\text{ and }
x=42$
Work Step by Step
Using the properties of equality, the given equation, $
5x^2=210x
,$ is equivalent to
\begin{align*}
5x^2-210x&=0
\\\\
\dfrac{5x^2-210x}{5}&=\dfrac{0}{5}
\\\\
x^2-42x&=0
\end{align*}
In the equation above, $a=
1
,$ $b=
-42
,$ and $c=
0
.$
Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}\require{cancel}x&=
\dfrac{-(-42)\pm\sqrt{(-42)^2-4(1)(0)}}{2(1)}
\\\\&=
\dfrac{42\pm\sqrt{1764-0}}{2}
\\\\&=
\dfrac{42\pm\sqrt{1764}}{2}
\\\\&=
\dfrac{42\pm42}{2}
\end{align*}
\begin{array}{lcl}
&\Rightarrow
\dfrac{42-42}{2} &\text{ OR }& \dfrac{42+42}{2}
\\\\&
=\dfrac{0}{2} && =\dfrac{84}{2}
\\\\&
=0 && =42
\end{array}
Hence, the solutions are $
x=0
\text{ and }
x=42
.$
