[tex] x^2-2m=\dfrac{k}{2}x\\
2x^2-4m=kx\\
2x^2-kx-4m=0\\\\
\Delta=(-k)^2-4\cdot2\cdot(-4m)=k^2+32m\\
\sqrt{\Delta}=\sqrt{k^2+32m}\\\\
x=\dfrac{-(-k)\pm \sqrt{k^2+32m}}{2\cdot2}=\dfrac{k\pm \sqrt{k^2+32m}}{4}=\dfrac{k}{4}\pm \dfrac{\sqrt{k^2+32m}}{4}
[/tex]
