Your question specifically asks for an equation which gives root radius and your sample equation is for typical root length, neither of which I'm aware of. However, there is a known relation between the above-ground biomass and the below-ground biomass of a plant, which varies with species and environmental factors. This is the root:shoot ratio.
This is a linear model where the constants represent differences in starting conditions (the intercept) and biomass partitioning (slope).
Roots and shoots are functionally interdependent and these two systems
maintain a dynamic balance in biomass which reflects relative
abundance of above-ground resources (light and CO2) compared with
root-zone resources (water and nutrients). Whole-plant growth rate and
root : shoot ratio are thus an outcome of genotype × environment
interaction, but source of control is ambiguous.
The actual size of the roots - as in their extent - will depend on the soil characteristics, water table, the plant species, etc.