\(x^2-5x-1=0\\a=1;\ b=-5;\ c=-1\\\\\Delta=b^2-4ac\\\Delta=(-5)^2-4\cdot1\cdot(-1)=25+4=29 \ \textgreater \ 0\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{29}\\\\x_1=\dfrac{-(-5)-\sqrt{29}}{2\cdot1}=\dfrac{5-\sqrt{29}}{2}\\\\x_2=\dfrac{-(-5)+\sqrt{29}}{2\cdot1}=\dfrac{5+\sqrt{29}}{2}\)
