#### Answer

no solution

#### Work Step by Step

Using the properties of equality, the given equation, $
3x^{1/2}+12=9
$, is equivalent to
\begin{array}{l}
3x^{1/2}=9-12
\\\\
3x^{1/2}=-3
\\\\
x^{1/2}=-\dfrac{3}{3}
\\\\
x^{1/2}=-1
.\end{array}
For any real number, the left side of the equal sign, $x^{1/2}$, always gives a positive number. This will never be equal to the negative expression on the right of the equal sign. Hence, there is $\text{
no solution.}$