Let's solve for the value of the discriminant for the given quadratic equation [tex]\(-3 = -x^2 + 2x\)[/tex].
### Step-by-Step Solution:
1. Rewrite the equation in standard form:
The standard form of a quadratic equation is [tex]\(ax^2 + bx + c = 0\)[/tex]. Starting from the given equation:
[tex]\[
-3 = -x^2 + 2x
\][/tex]
Add 3 to both sides to move all terms to one side of the equation:
[tex]\[
0 = -x^2 + 2x + 3
\][/tex]
Thus, the quadratic equation in standard form is:
[tex]\[
-x^2 + 2x + 3 = 0
\][/tex]
2. Identify the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]:
From the standard form equation [tex]\(-x^2 + 2x + 3 = 0\)[/tex], we can see that:
[tex]\[
a = -1, \quad b = 2, \quad c = 3
\][/tex]
3. Calculate the discriminant:
The discriminant of a quadratic equation [tex]\(ax^2 + bx + c = 0\)[/tex] is given by the formula:
[tex]\[
\Delta = b^2 - 4ac
\][/tex]
Substitute the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] into the formula:
[tex]\[
\Delta = 2^2 - 4(-1)(3)
\][/tex]
4. Simplify the expression:
[tex]\[
\Delta = 4 - (-12)
\][/tex]
Simplifying further:
[tex]\[
\Delta = 4 + 12
\][/tex]
[tex]\[
\Delta = 16
\][/tex]
### Conclusion:
The value of the discriminant for the quadratic equation [tex]\(-3 = -x^2 + 2x\)[/tex] is
[tex]\[
\boxed{16}
\][/tex]
