Question 19
The parabola $y=-x^2+2x+3$ meets the axes at $A$ and $B$ as shown. Point $E$ is on the positive $x$-axis. The vertical line through the midpoint of $OE$ meets $BE$ at $N$ and the parabola at $M$, with $MN=5/2$. The sum of all possible positive $x$-coordinates of $E$ is $a+b\sqrt c$, in simplified form with integers $a,b$ and square-free positive integer $c$. Find $abc$.
