Question 3 Solve the equation: \( 2 x^{2}+7 x+3=0 \)

To solve the quadratic equation \( 2x^{2}+7x+3=0 \), you can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Here, \( a = 2 \), \( b = 7 \), and \( c = 3 \). Plugging these values into the formula gives: 1. Calculate the discriminant: \( b^2 - 4ac = 7^2 - 4(2)(3) = 49 - 24 = 25 \). Since the discriminant is positive, there will be two real solutions. 2. Now plug this into the formula: \( x = \frac{-7 \pm \sqrt{25}}{2(2)} = \frac{-7 \pm 5}{4} \). 3. Solving this will yield two solutions: \( x_1 = \frac{-7 + 5}{4} = \frac{-2}{4} = -\frac{1}{2} \) \( x_2 = \frac{-7 - 5}{4} = \frac{-12}{4} = -3 \) So the solutions are \( x = -\frac{1}{2} \) and \( x = -3 \). Don't forget to check your work by plugging these values back into the original equation to verify they satisfy it—always a rewarding step to close the loop!