Atrast x
\left\{\begin{matrix}x\in \left(\frac{-\sqrt{24x_{0}+1}+1}{6},\frac{\sqrt{24x_{0}+1}+1}{6}\right)\text{, }&H>\frac{1}{6}\text{ and }x_{0}\leq \frac{3H^{2}-H}{2}\text{ and }x_{0}>-\frac{1}{24}\\x\in \left(\frac{-\sqrt{24x_{0}+1}+1}{6},H\right)\text{, }&\left(x_{0}>\frac{3H^{2}-H}{2}\text{ and }H<\frac{\sqrt{24x_{0}+1}+1}{6}\text{ and }x_{0}>-\frac{1}{24}\right)\text{ or }\left(H<\frac{\sqrt{24x_{0}+1}+1}{6}\text{ and }x_{0}>-\frac{1}{24}\text{ and }H\geq \frac{1}{6}\right)\end{matrix}\right,
Atrast x_0
x_{0}>\frac{x\left(3x-1\right)}{2}
x<H
Graph
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