Discriminant of a quadratic equation
Compute the value of the discriminant and give the number of real solutions of the quadratic equation.
\[
-2 x^{2}+3 x+8=0
\]
Discriminant:
Number of real solutions:

Step 1 ：Given the quadratic equation \(-2x^2 + 3x + 8 = 0\), we can identify the coefficients as \(a = -2\), \(b = 3\), and \(c = 8\).

Step 2 ：The discriminant of a quadratic equation is given by the formula \(D = b^2 - 4ac\).

Step 3 ：Substitute the values of \(a\), \(b\), and \(c\) into the formula to find the value of the discriminant: \(D = 3^2 - 4*(-2)*8 = 73\).

Step 4 ：The discriminant of the quadratic equation is \(\boxed{73}\).

Step 5 ：The number of real solutions of the quadratic equation depends on the value of the discriminant. If \(D > 0\), the equation has two distinct real solutions. If \(D = 0\), the equation has exactly one real solution. If \(D < 0\), the equation has no real solutions.

Step 6 ：Since the discriminant is greater than 0, the quadratic equation has two distinct real solutions.

Step 7 ：Final Answer: The discriminant of the quadratic equation \(-2x^2 + 3x + 8 = 0\) is \(\boxed{73}\), and the equation has \(\boxed{2}\) distinct real solutions.