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  • 2 years ago

What would be the best way to solve 3d^2+6d-1=0

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  1. jim_thompson5910
    • 2 years ago
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    Use the quadratic formula as it works with every quadratic (regardless of solution type) \[\Large d = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\] \[\Large d = \frac{-(6)\pm\sqrt{(6)^2-4(3)(-1)}}{2(3)}\] \[\Large d = \frac{-6\pm\sqrt{36-(-12)}}{6}\] \[\Large d = \frac{-6\pm\sqrt{48}}{6}\] \[\Large d = \frac{-6+\sqrt{48}}{6} \ \text{or} \ d = \frac{-6-\sqrt{48}}{6}\] \[\Large d = \frac{-6+4\sqrt{3}}{6} \ \text{or} \ d = \frac{-6-4\sqrt{3}}{6}\] \[\Large d = \frac{-3+2\sqrt{3}}{3} \ \text{or} \ d = \frac{-3-2\sqrt{3}}{3}\] So the solutions are \[\Large d = \frac{-3+2\sqrt{3}}{3} \ \text{or} \ d = \frac{-3-2\sqrt{3}}{3}\]

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