#### Answer

$x=\left\{ -2,9 \right\}$

#### Work Step by Step

Using the properties of equality, the given expression, $
x^2-2x=18+5x
,$ is equivalent to
\begin{array}{l}\require{cancel}
x^2-2x-5x-18=0
\\\\
x^2-7x-18=0
.\end{array}
Factoring the above equation, $
x^2-7x-18=0
,$ results to
\begin{array}{l}\require{cancel}
(x-9)(x+2)=0
.\end{array}
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
(x-9)(x+2)=0
,$ are
\begin{array}{l}\require{cancel}
x-9=0
\\\\
x=9
,\\\\\text{OR}\\\\
x+2=0
\\\\
x=-2
.\end{array}
Hence, $
x=\left\{ -2,9 \right\}
.$