(9) \( 2 x^{2}-5 x-3= \)

To solve the quadratic equation \( 2x^2 - 5x - 3 = 0 \), you can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Here, \( a = 2 \), \( b = -5 \), and \( c = -3 \). Plugging in these values, compute the discriminant \( b^2 - 4ac = (-5)^2 - 4(2)(-3) \), which simplifies to \( 25 + 24 = 49 \). Solving gives you two possible values for \( x \): \( 3 \) and \( -\frac{1}{2} \). Quadratic equations like this one pop up all the time in the real world! Whether you're calculating the trajectory of a basketball, optimizing a design in engineering, or even determining the best pricing strategy for a product, these equations help make sense of various scenarios. Understanding them can give you the edge to tackle problems in physics, economics, and beyond! When using the quadratic formula, remember to double-check your calculations—it's easy to make a mistake under pressure! Also, ensure that the discriminant is non-negative; if it’s negative, there are no real solutions. Lastly, always verify your answers by plugging them back into the original equation to see if they actually satisfy it. Happy solving!