Solve the Quadratic Equation: -5x² - 2x - 8 = 0

Let's solve the quadratic equation $-5x^2 - 2x - 8 = 0$ using the quadratic formula:

First, identify the coefficients: $a = -5$, $b = -2$, and $c = -8$.

The quadratic formula is given by:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

We start by calculating the discriminant, $D = b^2 - 4ac$:

$D = (-2)^2 - 4 \cdot (-5) \cdot (-8)$

$D = 4 - 160$

$D = -156$

Since the discriminant $D = -156$ is less than zero, this indicates that there are no real solutions for the quadratic equation $-5x^2 - 2x - 8 = 0$.

Therefore, the equation has no solution in terms of real numbers.