Find the roots of the quadratic equation \(3x^2 + 7x - 6 = 0\) using the quadratic formula.
Answer
Finally, compute the two roots of the equation: \(x = \frac{-7 + 11}{6}\) and \(x = \frac{-7 - 11}{6}\).
Step 1 ：The quadratic formula is given by \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). In this equation, \(a = 3\), \(b = 7\), and \(c = -6\).
Step 2 ：Substitute the values of \(a\), \(b\), and \(c\) into the quadratic formula: \(x = \frac{-7 \pm \sqrt{7^2 - 4*3*(-6)}}{2*3}\).
Step 3 ：Simplify the expression inside the square root: \(x = \frac{-7 \pm \sqrt{49 - (-72)}}{6}\).
Step 4 ：Further simplify the expression: \(x = \frac{-7 \pm \sqrt{121}}{6}\).
Step 5 ：Finally, compute the two roots of the equation: \(x = \frac{-7 + 11}{6}\) and \(x = \frac{-7 - 11}{6}\).
