Discriminant of a quadratic equation
Compute the value of the discriminant and give the number of real solutions of the quadratic equation.
$$-2x^2+3x+8=0$$
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: $D=3^2-4\ast (-2)\ast 8=73$.

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

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 $\boxed{{\displaystyle 73}}$, and the equation has $\boxed{{\displaystyle 2}}$ distinct real solutions.