The ratio of mass of the earth to mass of the moon is 82.4, so the ratio of the distance from the center of the earth to the center of mass and the distance from the center of the moon to the center of mass is 1/82.4. So the distance from the center of earth to the center of mass will be 1/(82.4 + 1) * 387000 = roughly 4630 kilometers. Which means the center of mass lies under the surface of the earth.
Interesting. Without checking it, my first thought is that the Moon's gravitational effect on Earth's oceans is part of your equation's meaning, and (quoting Steve Jones again) ...
The atlas of the past holds many surprises. To reconstruct it, all that is needed is to subtract from the map of today the ocean floor made since the date in question. The key is the Earth's magnetic field. Every few hundred thousand years, what was the North Pole becomes the South until the poles reverse once more in their endless dance. The switch is recorded in the rocks. Great stripes of magnetic reversal across the bottom of the ocean mark their movements."