2x²+7x-6=0

To solve the quadratic equation \(2x^2 + 7x - 6 = 0\), we can use the quadratic formula, which is given by: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] In this equation, \(a = 2\), \(b = 7\), and \(c = -6\). First, we will calculate the discriminant (\(D\)): \[ D = b^2 - 4ac = 7^2 - 4 \cdot 2 \cdot (-6) \] \[ D = 49 + 48 = 97 \] Next, we will plug the values into the quadratic formula: \[ x = \frac{-7 \pm \sqrt{97}}{2 \cdot 2} \] \[ x = \frac{-7 \pm \sqrt{97}}{4} \] Thus, the solutions for the equation \(2x^2 + 7x - 6 = 0\) are: \[ x = \frac{-7 + \sqrt{97}}{4} \quad \text{and} \quad x = \frac{-7 - \sqrt{97}}{4} \] These are the two roots of the quadratic equation.