We are given:
\(\displaystyle{x}²-{5}{x}={18}+{2}{x}\)

Write in the form \(\displaystyle{a}{x}²+{b}{x}+{c}={0}\)

\(\displaystyle{x}²-{7}{x}-{18}={0}\)

Factor the left side: (x+2)(x-9)=0

By zero product property, x+2=0 and x-9=0

x=-2 and x=9

Write in the form \(\displaystyle{a}{x}²+{b}{x}+{c}={0}\)

\(\displaystyle{x}²-{7}{x}-{18}={0}\)

Factor the left side: (x+2)(x-9)=0

By zero product property, x+2=0 and x-9=0

x=-2 and x=9