Answer: [tex]\bold{\dfrac{1\pm \sqrt{11}}{2}}[/tex]
Step-by-step explanation:
[tex]x^2-x-\frac{5}{2}=0\quad \text{multiply by 2 to get:}\\\\2x^2-2x-5=0\quad \rightarrow \quad a=2,\ b=-2,\ c=-5\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-2)\pm \sqrt{(-2)^2-4(2)(-5)}}{2(2)}\\\\\\.\ =\dfrac{2\pm \sqrt{40}}{2(2)}\\\\\\.\ =\dfrac{2\pm \sqrt{44}}{2(2)}\\\\\\.\ =\dfrac{2\pm 2\sqrt{11}}{2(2)}\\\\\\.\ =\boxed{\dfrac{1\pm \sqrt{11}}{2}}[/tex]
