To solve the equation \(3x^2 = 21\), we first divide both sides by 3:
\[ x^2 = \frac{21}{3} \]
This simplifies to:
\[ x^2 = 7 \]
Next, we take the square root of both sides. Remember that taking the square root of a number produces both a positive and a negative solution:
\[ x = \sqrt{7} \quad \text{and} \quad x = -\sqrt{7} \]
Thus, there are two solutions: \(x = \sqrt{7}\) and \(x = -\sqrt{7}\).
Therefore, the answer is two.