To solve the quadratic equation \(3x^2 = -72\), we first rearrange it:
\[ 3x^2 + 72 = 0 \]
Next, we divide all terms by 3:
\[ x^2 + 24 = 0 \]
Now, we can isolate \(x^2\):
\[ x^2 = -24 \]
Next, we take the square root of both sides. Remember that the square root of a negative number involves imaginary numbers:
\[ x = \pm \sqrt{-24} \] \[ x = \pm \sqrt{24}i \] \[ x = \pm \sqrt{4 \cdot 6}i \] \[ x = \pm 2\sqrt{6}i \]
Thus, the solutions to the equation are:
\[ x = \pm 2\sqrt{6}i \]
Looking at the options provided:
- A: \(-24-24−24\)
- B: \(\pm 26 \pm 2\sqrt{6} \pm 2\)
- C: \(\pm 6i \sqrt{2} \pm 6i\)
- D: \(\pm 2i \sqrt{6} \pm 2i\)
The correct solution matches with:
\[ \text{D: } \pm 2i \sqrt{6} \]
So, the answer is D.