GIVEN
The equation is given to be:
[tex]\sqrt{-3u+18}=u[/tex]
SOLUTION
To solve for u.
Square both sides of the equation:
[tex]\begin{gathered} -3u+18=u^2 \\ Rearrange \\ u^2+3u-18=0 \end{gathered}[/tex]
Solve the quadratic equation by factorization:
[tex]\begin{gathered} u^2+3u-18=0 \\ Rewrite \\ u^2+6u-3u-18=0 \\ Factor \\ u(u+6)-3(u+6)=0 \\ Factor\text{ }again \\ (u+6)(u-3)=0 \\ \mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0 \\ \therefore \\ u+6=0,u=-6 \\ or \\ u-3=0,u=3 \end{gathered}[/tex]
Check the solutions if it satisfies the equation:
[tex]\begin{gathered} u=-6 \\ \sqrt{-3(-6)+18}=-6 \\ \sqrt{36}=-6 \\ 6=-6\text{ \lparen False\rparen} \\ \\ u=3 \\ \sqrt{-3(3)+18}=3 \\ \sqrt{9}=3 \\ 3=3\text{ \lparen True\rparen} \end{gathered}[/tex]
Therefore, the solution to the equation is:
[tex]u=3[/tex]
