3x² + 6x = 420

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• Try brute-force: let x = smallest, then x² + (x+1)² + (x+2)² = 425
• x² + x² + 2x + 1 + x² + 4x + 4 = 425
• 3x² + 6x + 5 = 425
• x² + 2x = 140
• x² + 2x - 140 = 0
• Discriminant: \( 4 + 560 = 564 \) → not a perfect square → no integer solution?

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