What is the beta decay equations?

Beta decay occurs when a neutron located in the nucleus of a radioactive isotope is converted into a proton by the emission of an electron.
In addition to the electron, or $\beta$-particle, an electron neutrino is also emitted from the nucleus.
Since a neutron is converted into a proton, the atomic number of the element will Increase by 1. At the same time, the mass number will be left unchanged.
You can write the general equation for beta decay like this.

Notice that the atomic number, $Z$, increased by $1$, and the mass number, $A$, remained unchanged. You can use that equation to describe the beta decay of any nuclide.
For example, the beta decay of carbon-14 will look like this
${}_6^{14}\mathrm{C}\to {}_7^{14}\mathrm{N}+{}_{-1}^{0}e+{}_0^0{\bar{\nu }}_e$