To solve the equation \(3x^2 = 21\), we can start by dividing both sides of the equation by 3:
\[ x^2 = \frac{21}{3} \] \[ x^2 = 7 \]
Next, to find \(x\), we take the square root of both sides:
\[ x = \pm \sqrt{7} \]
This means there are two solutions: \(x = \sqrt{7}\) and \(x = -\sqrt{7}\).
Thus, the solution set has two solutions.
The answer is C. Two.