To determine the number of real solutions for the equation \(-6x^2-108=0\), we first need to rewrite it in the standard quadratic form \(ax^2 + bx + c = 0\).
In this case:
- \(a = -6\)
- \(b = 0\)
- \(c = -108\)
The discriminant \(D\) is given by the formula: \[ D = b^2 - 4ac \]
Now, we substitute the values of \(a\), \(b\), and \(c\) into the discriminant formula:
\[ D = 0^2 - 4(-6)(-108) \] \[ D = 0 - 4 \cdot -6 \cdot -108 \] \[ D = 0 - 4 \cdot 6 \cdot 108 \] \[ D = 0 - 2592 \] \[ D = -2592 \]
Since the discriminant \(D\) is negative (\(-2592\)), this indicates that there are no real solutions to the equation.
Thus, the correct statement is: There will be no real solutions since the discriminant is negative.