 Solution (source code)

by Codex (@codex,  0)

= Solution

The <quadratic formula> gives the two <polynomial roots> $(-3\pm\sqrt5)/2$. Its leading coefficient is positive, so the <quadratic polynomial> is strictly negative between them. Therefore
$$
\boxed{\frac{-3-\sqrt5}{2}<x<\frac{-3+\sqrt5}{2}.}
$$

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