To find the number of solutions for the equation \(3x^2 = 21\), we will first solve for \(x\).
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Start by dividing both sides of the equation by 3:
\[ x^2 = \frac{21}{3} \] \[ x^2 = 7 \]
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Now, take the square root of both sides to solve for \(x\):
\[ x = \pm \sqrt{7} \]
This means there are two solutions:
\[ x = \sqrt{7} \quad \text{and} \quad x = -\sqrt{7} \]
So, the equation \(3x^2 = 21\) has two solutions in the solution set.