The chemical equations for the detection of nickel using the borax bead test are as follows: First, borax is heated to form a glassy bead of sodium metaborate and boron trioxide: $$ \begin{aligned} Na_2B_4O_7 \cdot 10H_2O &\xrightarrow{\Delta} 2NaBO_2 + B_2O_3 + 10H_2O \end{aligned} $$ Nickel sulfate is heated to form nickel oxide: $$ \begin{aligned} NiSO_4 &\xrightarrow{\Delta} NiO + SO_2 + O_2 \end{aligned} $$ The nickel oxide then reacts with the borax bead components to form nickel metaborate, which appears as a reddish-brown bead: $$ \begin{aligned} NiO + NaBO_2 &\rightarrow NiNaBO_3 \\ NiO + B_2O_3 &\rightarrow Ni(BO_2)_2 \end{aligned} $$ These products result in the characteristic reddish-brown color of the bead.