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james comer and his college roommate - ECD Germany

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Calculate the discriminant: \( b^2 - 4ac = (-12)^2 - 4 \times 3 \times 9 = 144 - 108 = 36 \).

📌 So, \( x = \frac{12 \pm \sqrt{36}}{6} = \frac{12 \pm 6}{6} \).

📌 This gives \( x = \frac{18}{6} = 3 \) and \( x = \frac{6}{6} = 1 \).

📌 The formula for the sum is \( S = \frac{n(n+1)}{2} \).

📌 Set \( \frac{n(n+1)}{2} = 210 \). Multiply through by 2: \( n(n+1) = 420 \).

📌 Solve the quadratic equation: \( n^2 + n - 420 = 0 \).

📌 Using the quadratic formula: \( n = \frac{-1 \pm \sqrt{1 + 4 \times 420}}{2} = \frac{-1 \pm \sqrt{1681}}{2} \).

📌 Since \( \sqrt{1681} = 41 \), \( n = \frac{-1 + 41}{2} = 20 \) (only positive solution).

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