Use the discriminant to tell whether the solutions of this equation are real or complex \[ 2 x^{2}+3 x+(-4)=0 \]

To determine if the solutions of the quadratic equation \( 2x^2 + 3x - 4 = 0 \) are real or complex, we can use the discriminant formula, which is given by \( D = b^2 - 4ac \). In this case, \( a = 2 \), \( b = 3 \), and \( c = -4 \). Plugging these values into the formula, we get: \[ D = (3)^2 - 4(2)(-4) = 9 + 32 = 41 \] Since the discriminant \( D \) is greater than 0, the equation has two distinct real solutions! Now you're ready to solve for those solutions using the quadratic formula \( x = \frac{-b \pm \sqrt{D}}{2a} \) if you're feeling adventurous!