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Answer:
[tex]x_1=\frac{5+\sqrt{33}}{4}\approx2.6861\\ \\x_2=\frac{5-\sqrt{33}}{4}\approx-0.1861[/tex]
Step-by-step explanation:
[tex]2x^2-5x-1=0\\\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\x=\frac{-(-5)\pm\sqrt{(-5)^2-4(2)(-1)}}{2(2)}\\ \\x=\frac{5\pm\sqrt{25+8}}{4}\\ \\x=\frac{5\pm\sqrt{33}}{4}\\ \\x_1=\frac{5+\sqrt{33}}{4}\approx2.6861\\ \\x_2=\frac{5-\sqrt{33}}{4}\approx-0.1861[/tex]