To solve the equation \( 3x^2 = 21 \), we first divide both sides by 3:
\[ x^2 = 7 \]
Next, we take the square root of both sides:
\[ x = \sqrt{7} \quad \text{or} \quad x = -\sqrt{7} \]
This gives us two solutions: \( \sqrt{7} \) and \( -\sqrt{7} \).
Thus, the number of solutions in the solution set for the equation \( 3x^2 = 21 \) is:
two.