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Home » x^2 - 2x + 3x - 6 = x^2 + x - 6 - High Altitude Science

x^2 - 2x + 3x - 6 = x^2 + x - 6 - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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Solve for x: \( 3x^2 - 12x + 9 = 0 \).
The quadratic formula is \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).
Here, \( a = 3 \), \( b = -12 \), \( c = 9 \).
Calculate the discriminant: \( b^2 - 4ac = (-12)^2 - 4 \times 3 \times...
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) = 4...
Solve the quadratic equation: \( n^2 + n - 420 = 0 \).
Using the quadratic formula: \( n = \frac{-1 \pm \sqrt{1 + 4 \times 42...

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