Given the quadratic equation:
[tex]2x{}^2-1x-2=0[/tex]
We can use the general solution for the quadratic equation ax² + bx + c = 0:
[tex]x=\frac{-b\pm\sqrt{b{}^2-4ac}}{2a}[/tex]
From the problem, we identify:
[tex]\begin{gathered} a=2 \\ b=-1 \\ c=-2 \end{gathered}[/tex]
Finally, using the general solution:
[tex]\begin{gathered} x=\frac{-(-1)\pm\sqrt{(-1)^2-4(2)(-2)}}{2\cdot2}=\frac{1\pm\sqrt{1+16}}{4} \\ \\ \therefore x=\frac{1\pm\sqrt{17}}{4} \end{gathered}[/tex]
