Editing Equation solving (section)

===Polynomial equations===
{{Main|Polynomial#Solving polynomial equations|l1=Solving polynomial equations}}
{{see also|System of polynomial equations}}
[[Polynomial]] equations of degree up to four can be solved exactly using algebraic methods, of which the [[quadratic formula]] is the simplest example. Polynomial equations with a degree of five or higher require in general numerical methods (see below) or special functions such as [[Bring radical]]s, although some specific cases may be solvable algebraically, for example
:<math>4x^5 - x^3 - 3 = 0</math>
(by using the [[rational root theorem]]), and
:<math>x^6 - 5x^3 + 6 = 0 \, ,</math>
(by using the substitution {{math|''x'' {{=}} ''z''<sup>{{frac|1|3}}</sup>}}, which simplifies this to a [[quadratic equation]] in {{mvar|z}}).