$x^2(\frac{1}{1}+\frac{1}{2}+...\frac{1}{2024})+2024=2024$ $x^2(\frac{1}{1}+\frac{1}{2}+...\frac{1}{2024})=0$ $x=0$

let $ x^2=w$ $$\frac{w + 1}{1} + \frac{w+ 2}{2} + \frac{w + 3}{3} + \ldots + \frac{w + 2024}{2024} = 2024 $$Equation wrt $w$ , is first degree, has real solution $w=0$ and has not solution $w=100$ as first part of equation has $2024$ positive terms greater than$ 1$ and therefore their sum cannot be equal to $2024$. So $ w=0$ is the only solution, so $x^2=0 \Leftrightarrow x=0$