I was tasked in my programming lesson to find a value of L1 correct to 5 significant figures, but in my discussion section I began to wonder why there was no second solution to the equation I was trying to find the root of (L2). The equation was $$\frac{GM}{x^2}-\frac{Gm}{(R-x)^2}-w^2x=0.$$ Where $M$ was the mass of the Earth, $m$ was the mass of the moon, $x$ was the distance from the earth to the satellite, $R$ was the distance to the moon and $w$ is the angular velocity of the moon.
My question is, along the line connecting the earth and the moon there should be 2 points where the net force is pointing towards the Earth with a magnitude that gives the net accleration to be the same as the moon's. These points are what I understand to be L1 and L2. From my code only L1 was found. I plot the function on desmos and saw this:
According to desmos, there was no L2 point.
Is this because of my assumption that the orbits are circular? How does one find L2?