Answer: You have the correct answer. It's choice C.
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Work Shown:
[tex]3n^2+5 = -46\\\\3n^2 = -46-5\\\\3n^2 = -51\\\\n^2 = -51/3\\\\n^2 = -17\\\\n = \pm\sqrt{-17}\\\\n = \sqrt{-17} \ \text{ or } \ n = -\sqrt{-17}\\\\n = \sqrt{-1*17} \ \text{ or } \ n = -\sqrt{-1*17}\\\\n = \sqrt{-1}*\sqrt{17} \ \text{ or } \ n = -\sqrt{-1}*\sqrt{17}\\\\n = i\sqrt{17} \ \text{ or } \ n = -i\sqrt{17}\\\\[/tex]
where [tex]i= \sqrt{-1}[/tex] is the imaginary number.
The quadratic formula is another option you could do and you should get the same answers as above.
