Marinada '21

[lang=hr] Jednadžba $x^3 + 2x^2 + 3x + 4 = 0$ ima jedno realno rješenje koje možemo napisati u obliku \[ x = \frac{\sqrt[3]{-a+b\sqrt{c}} - \sqrt[3]{a+b\sqrt{c}} - d}{e} \] pri čemu su $a$, $b$, $c$, $d$ i $e$ prirodni brojevi, a dani izraz je do kraja skraćen i djelomično korjenovan. \\ Koliko iznosi $a + b + c + d + e$? [/lang] [lang=en] The equation $x^3 + 2x^2 + 3x + 4 = 0$ has one real solution which can be expressed in the following way: \[ x = \frac{\sqrt[3]{-a+b\sqrt{c}} - \sqrt[3]{a+b\sqrt{c}} - d}{e} \] where $a$, $b$, $c$, $d$ and $e$ are natural numbers and the expression above (fraction and radicals) is in simplest form. \\ Find $a + b + c + d + e$. [/lang]