Marinada '25

[lang=hr] Za svoj finalni zadatak, Ivica mora biti siguran da će Maricu oborit s nogu. Upravo zato, smislio je najljepši i najteži zadatak do sasd te on glasi ovako: Neka $m$ bude najveće realno rješenje sljedeće jednadžbe: \[ \frac{5}{x-5}+\frac{7}{x-7}+\frac{17}{x-17}+\frac{19}{x-19}=x^2-12x-4 \] Taj $m$ se može zapisati kao $a+\sqrt{b+\sqrt{c}}$ pri ćemu su $a,b,c$ cijeli brojevi. Koliko je $a+b+c$? [/lang] [lang=en] For his final assignment, Ivica wants to be absolutely sure that Marica will fall for him. Therefore, he devised the most beautiful and hardest problem ever, which reads as follows: Let $m$ be the largest real solution of the equation $$ \frac{5}{x-5}+\frac{7}{x-7}+\frac{17}{x-17}+\frac{19}{x-19}=x^{2}-12x-4 . $$ This number $m$ can be expressed in the form $a + \sqrt{b + \sqrt{c}} $ where $a$, $b$, and $c$ are integers. Find the value of $a + b + c$. [/lang]