Answer:
[tex]x_1=\dfrac{5-\sqrt{57}}{2}\ ,\quad x_2=\dfrac{5+\sqrt{57}}{2}[/tex]
Step-by-step explanation:
[tex]x^2-5x-8=0\\\\a=1\,,\ b=-5\,,\ c=-8\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-(-5)\pm\sqrt{(-5)^2-4\cdot1\cdot(-8)}}{2\cdot1}=\dfrac{5\pm\sqrt{25+32}}{2}=\dfrac{5\pm\sqrt{57}}{2}[/tex]
