\(25x+6x^2>80\)
\(\Leftrightarrow6x^2+25x-80>0\)
\(\Leftrightarrow\left(\sqrt{6}x\right)^2+2\cdot\sqrt{6}x\cdot\dfrac{25\sqrt{6}}{12}+\dfrac{625}{24}-\dfrac{2545}{24}>0\)
\(\Leftrightarrow\left(\sqrt{6}x+\dfrac{25\sqrt{6}}{12}\right)^2-\dfrac{2545}{24}>0\)
\(\Leftrightarrow\left(\sqrt{6}x+\dfrac{25\sqrt{6}}{12}-\sqrt{\dfrac{2524}{24}}\right)\left(\sqrt{6}x+\dfrac{25\sqrt{6}}{12}+\sqrt{\dfrac{2524}{24}}\right)>0\)
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