Shortest Troll Bridge Span

Calculus Level 5

The coastline

as shown in this map of a coastal inlet entrance is described by the following equation

$$9\left( { x }^{ 2 }-y \right) \left( x-1 \right) +2=0$$

where $$1$$ equals $$1,000$$ feet.

The port city, in brown, needs to build a bridge straight across the inlet entrance. What's the shortest possible span, to the nearest integer number of feet?

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