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A quadratic equation is given by \(2x^2 - 4x - 6 = 0\). Solve for \(x\) using the quadratic formula.
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The quadratic formula is given by \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).
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For the equation \(2x^2 - 4x - 6 = 0\) we identify \(a = 2\) \(b = -4\) \(c = -6\).
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First calculate the discriminant: \(\Delta = b^2 - 4ac = (-4)^2 - 4 \times 2 \times (-6) = 16 + 48 = 64\).
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Since the discriminant is positive there are two real solutions:
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\(x = \frac{-(-4) \pm \sqrt{64}}{2 \times 2} = \frac{4 \pm 8}{4}\).
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