Editing Equation (section)

{{Short description|Mathematical formula expressing equality}}
{{other uses}}{{Expand French}}[[File:First Equation Ever.png|thumb|right|300px|The first use of an equals sign, equivalent to 14''x'' + 15 = 71 in modern notation. From ''[[The Whetstone of Witte]]'' by [[Robert Recorde]] of Wales (1557).<ref name="Whetstone">Recorde, Robert, ''The Whetstone of Witte'' ... (London, England: {{not a typo|Jhon}} Kyngstone, 1557), [https://archive.org/stream/TheWhetstoneOfWitte#page/n237/mode/2up the third page of the chapter "The rule of equation, commonly called Algebers Rule."]</ref>]]

In [[mathematics]], an '''equation''' is a [[mathematical formula]] that expresses the [[equality (mathematics)|equality]] of two [[Expression (mathematics)|expressions]], by connecting them with the [[equals sign]] {{char|1==}}.<ref name=":1">{{Cite web|title=Equation - Math Open Reference|url=https://www.mathopenref.com/equation.html|access-date=2020-09-01|website=www.mathopenref.com}}</ref><ref>{{Cite web|title=Equations and Formulas|url=https://www.mathsisfun.com/algebra/equation-formula.html|access-date=2020-09-01|website=www.mathsisfun.com}}</ref> The word ''equation'' and its [[cognate]]s in other languages may have subtly different meanings; for example, in [[French language|French]] an ''équation'' is defined as containing one or more [[variable (mathematics)|variables]], while in [[English language|English]], any [[well-formed formula]] consisting of two expressions related with an equals sign is an equation.<ref>{{cite web |last1=Marcus |first1=Solomon |last2=Watt |first2=Stephen M. |title=What is an Equation? |url=https://www.academia.edu/3287674 |access-date=2019-02-27 |author1-link=Solomon Marcus }}</ref>

[[Equation solving|Solving an equation]] containing variables consists of determining which values of the variables make the equality true. The variables for which the equation has to be solved are also called '''unknowns''', and the values of the unknowns that satisfy the equality are called [[solution (equation)|solutions]] of the equation. There are two kinds of equations: [[identity (mathematics)|identities]] and conditional equations. An identity is true for all values of the variables. A conditional equation is only true for particular values of the variables.<ref>{{cite book
 |chapter-url=http://www.universalis.fr/encyclopedie/NT01240/EQUATION_mathematique.htm
 |chapter=Équation, mathématique
 |first=Gilles|last=Lachaud
 |title=Encyclopædia Universalis
 |date=29 January 2025
 |language=fr
}}</ref><ref>"A statement of equality between two expressions. Equations are of two types, '''identities''' and '''conditional equations''' (or usually simply "equations")". « ''Equation'' », in ''{{Lang|en|Mathematics Dictionary}}'', {{ill|Glenn James (mathematician)|lt=Glenn James|de|Glenn James}} et [[Robert C. James]] (éd.), Van Nostrand, 1968, 3 ed. 1st ed. 1948, {{p.|131}}.</ref>

The "[[=]]" symbol, which appears in every equation, was invented in 1557 by [[Robert Recorde]], who considered that nothing could be more equal than parallel straight lines with the same length.<ref name="Whetstone" />