> No idea what equations are used for getting to the result

"Basic" gravitational equations applied to observed behaviour: clumping and rotation of galaxies, lensing (light bending), etc.

The behaviour implies "something" is exerting force in a mass like way - but there's a shortfall of visible mass.

The observational hole left by the apparent behaviour of "unseen matter" attracts a lot of theory.

* Physics "allows for" various types of particles with various types of properties - these may or may not all exist, some do. eg: Neutrino's from the sun barely interact with anything, consistently capturing them is a challenge. Maybe Dark Matter is a new hard to observe gravity particle.

* Physics has equations formed by "human scale" observation and sometimes tweaked for scales beyond direct human experience. eg: relativistic tweaks related to speeds approaching that of light. Maybe Dark Matter is a warping of observation at galaxy scale.

The opening paragraphs of, say, https://en.wikipedia.org/wiki/Dark_matter cover the ground of speculation.