`(2x+1)(x-3)<2`
`<=>2x^2-6x+x-3<2`
`<=>2x^2-5x-3<2`
`<=>2x^2-5x-5<0`
`<=>2x^2-5x+25/8-65/8<0`
`<=>(x\sqrt2-5/{2\sqrt2})^2-(\sqrt65/{2\sqrt2})^2<0`
`<=>(x\sqrt2-5/{2\sqrt2}-\sqrt65/{2\sqrt2})(x\sqrt2-5/{2\sqrt2}+\sqrt65/{2\sqrt2})<0`
`<=>(x\sqrt2-{5+\sqrt65}/{2\sqrt2})(x\sqrt2-{5-\sqrt65}/{2\sqrt2})<0`
Do `x\sqrt2-{5+\sqrt65}/{2\sqrt2}<x\sqrt2-{5-\sqrt65}/{2\sqrt2}`
`=>`$\left\{\begin{matrix}x\sqrt2-\dfrac{5+\sqrt{65}}{2\sqrt2}<0\\x\sqrt2-\dfrac{5-\sqrt{65}}{2\sqrt2}>0\end{matrix}\right.$
`<=>`$\left\{\begin{matrix}x\sqrt2<\dfrac{5+\sqrt{65}}{2\sqrt2}\\x\sqrt2>\dfrac{5-\sqrt{65}}{2\sqrt2}\end{matrix}\right.$
`<=>`$\left\{\begin{matrix}x<\dfrac{5+\sqrt{65}}4\\x>\dfrac{5-\sqrt{65}}{4}\end{matrix}\right.$
Hay `{5-\sqrt65}/4<x<{5+\sqrt65}/4`
