Solve the Quadratic Equation: -2x² - 5x - 9 = 0

Solve the following equation:

$-2x^2-5x-9=0$

To solve the quadratic equation $-2x^2 - 5x - 9 = 0$, we follow these steps:

• Step 1: Identify coefficients $a = -2$, $b = -5$, $c = -9$.
• Step 2: Compute the discriminant, $b^2 - 4ac$.
• Step 3: Analyze the discriminant's value to determine the nature of the roots.

Step 1: We have $a = -2$, $b = -5$, $c = -9$.

Step 2: Calculate the discriminant:
$b^2 - 4ac = (-5)^2 - 4(-2)(-9) = 25 - 72 = -47$.

Step 3: Since the discriminant value is $-47$, which is less than zero, this indicates that there are no real solutions because the square root of a negative number is imaginary.

Therefore, since there are no real solutions, we conclude that the problem has no real solutions.

Thus, the solution to the equation is No solution.