Solution of single parameter Bring quintic equation

In this paper, we propose a new method to obtain a solution to a single-parameter Bring quintic equation of the form, $x^5+x=a$, where $a$ is real. The method transforms the given quintic equation to an infinite but convergent series expression in $(x\mathrm{/}a)$, which is further transformed to a quartic equation in a novel fashion. The coefficients of the quartic equation so obtained are some kind of infinite series expressions in $a^{-4}$, which are termed as $\mathit{\text{ultraradicals}}$. The quartic equation is then solved and its one real solution is picked; further using this, the real solution of quintic equation, $x^5+x=a,$ is extracted. The ultraradicals used in this method converge for $\mathrm{\mid }a\mathrm{\mid }>1$; hence the method can be used when $\mathrm{\mid }a\mathrm{\mid }>1$.