A particle of charge q and mass m is subjected to an electric field...

${W}_{ex} = \Delta K{K}_{1} - {K}_{1} = 0$

${∫}_{0}^{x}qEdx = 0$

$\text{q}{∫}_{0}^{x}{E}_{0}\left(1 - {Qx}^{2}\right)dx = 0$

${qE}_{0}{∫}_{0}^{x}\left(1 - {ax}^{2}\right)dx = 0$

$x - \dfrac{{ax}^{3}}{3} = 0$

$1 - \dfrac{{ax}^{2}}{3} = 0$

$\dfrac{{ax}^{2}}{3} = 1$

${x}^{2} = \dfrac{3}{a}$

$x = \sqrt{\dfrac{3}{a}}$