ANSWER
[tex]C.\text{ }3x^2+2=0[/tex]
EXPLANATION
We want to identify the equations that have complex roots.
For an equation to have complex roots, the following condition must be satisfied:
[tex]b^2-4ac<0[/tex]
where a = leading coefficient
b = coefficient of x
c = constant term
Let us test for each equation.
For option A:
[tex]\begin{gathered} 3x^2-1=6x \\ \\ 3x^2-6x-1=0 \\ \\ a=3,\text{ }b=-6,\text{ }c=-1 \\ \\ (-6)^2-(4*3*-1) \\ \\ 36+12 \\ \\ 48 \end{gathered}[/tex]
Since this value is not less than 0, it does not have complex roots.
For option B:
[tex]\begin{gathered} 2x^2-1=5x \\ \\ 2x^2-5x-1=0 \\ \\ a=2,\text{ }b=-5,\text{ }c=-1 \\ \\ (-5)^2-(4*2*-1) \\ \\ 25+8 \\ \\ 33 \end{gathered}[/tex]
It does not have complex roots.
For option C:
[tex]\begin{gathered} 3x^2+2=0 \\ \\ a=3,\text{ }b=0,\text{ }c=2 \\ \\ (0)^2-(4*3*2) \\ \\ 0-24 \\ \\ -24 \end{gathered}[/tex]
Since this value is less than 0, it has complex roots.
Therefore, the correct option is option C.
