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\( n = \frac{-1 \pm \sqrt{1 + 1680}}{2} = \frac{-1 \pm \sqrt{1681}}{2} = \frac{-1 \pm 41}{2} \)
Taking the positive solution: \( n = \frac{40}{2} = 20 \).
A train travels 300 km at a speed of 60 km/h and then another 200 km at a speed of 80 km/h. What is the train's average speed for the entire journey?
Time for first part: \( \frac{300}{60} = 5 \) hours.
Time for second part: \( \frac{200}{80} = 2.5 \) hours.
Total distance: \( 300 + 200 = 500 \) km.
Total time: \( 5 + 2.5 = 7.5 \) hours.
Average speed: \( \frac{500}{7.5} = 66.67 \) km/h.
#### 66.67
Solve for \( x \): \( 3x^2 - 12x + 9 = 0 \).