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Answer:
To find the value of the discriminant for the quadratic equation \(-3 = -x^2 + 2x\), we first need to rewrite the equation in the standard form \(ax^2 + bx + c = 0\).
Starting with:
\[ -3 = -x^2 + 2x \]
Rearrange it to the standard form:
\[ -x^2 + 2x + 3 = 0 \]
Now, identify the coefficients:
\[ a = -1, \quad b = 2, \quad c = 3 \]
The formula for the discriminant (\(\Delta\)) is:
\[ \Delta = b^2 - 4ac \]
Plug in the values of \(a\), \(b\), and \(c\):
\[ \Delta = (2)^2 - 4(-1)(3) \]
\[ \Delta = 4 + 12 \]
\[ \Delta = 16 \]
So, the value of the discriminant is:
\[ 16 \]
Therefore, the correct answer is 16.