[tex]6x^2+5x-1=0\\\\a=6, \ \ \ b=5, \ \ c=-1 \\\\x_{1}=\frac{-b-\sqrt{b^2-4ac}}{2a}=\frac{-5-\sqrt{5^2-4 \cdot 6\cdot (-1) }}{2*6}= \frac{-5-\sqrt{25+24 }}{12}= \frac{-5-\sqrt{49}}{12}=\\\\= \frac{-5-7}{12}=\frac{ -12}{12}=-1[/tex]
[tex]x_{2}=\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-5+\sqrt{5^2-4 \cdot 6\cdot (-1) }}{2*6}= \frac{-5+7}{12}=\frac{ 2}{12}= \frac{1}{6}[/tex]
