Answer: To solve the quadratic equation \(3x^2 - 8x - 3 = 0\), we can use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In this equation, \(a = 3\), \(b = -8\), and \(c = -3\). Plugging these values into the quadratic formula gives:
\[ x = \frac{-(-8) \pm \sqrt{(-8)^2 - 4 \cdot 3 \cdot (-3)}}{2 \cdot 3} \]
\[ x = \frac{8 \pm \sqrt{64 + 36}}{6} \]
\[ x = \frac{8 \pm \sqrt{100}}{6} \]
\[ x = \frac{8 \pm 10}{6} \]
This results in two solutions:
1. \( x = \frac{8 + 10}{6} = \frac{18}{6} = 3 \)
2. \( x = \frac{8 - 10}{6} = \frac{-2}{6} = -\frac{1}{3} \)
Thus, the solutions to the quadratic equation \(3x^2 - 8x - 3 = 0\) are:
\[ x = 3 \quad \text{and} \quad x = -\frac{1}{3} \]
Step-by-step explanation:
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