Equation, statement of equality. Mathematical equations are often expressed in algebraic notation, where known and unknown quantities can be represented by symbols. Notations of branches of mathematics such as differential calculus or logic can also be used to represent relationships of equality. Other disciplines have created shorthand notations representing equalities, as in chemistry, where chemical equations represent chemical reactions. One of the most familiar forms of equations in mathematics is the n degree polynomial equation (of order n):
axn+bxn−1+cxn−2+ z =0
Here x is a variable denoting an unknown quantity and a, b, c z represent known values.
If n=2, the generalized form reduces to a quadratic equation: ax2+bx+c=0. Such equations have 2 solutions or roots:
Because these examples have only one unknown variable, solutions can be found. Equations can have more than one unknown. In such cases there must be as many equations as there are variables in order to solve for the unknowns. Consider the equation: 2x+xy+3=0. Without additional information it is impossible to determine either x or y explicitly. However, with the additional information of another equation such as: x+2xy=0, finding values for both variables x and y that simultaneously satisfy each equation of the system is possible. By mathematical manipulation the solution to the system made up of the 2 equations is: x=−2 and y=−1/2. the formulation and solving of systems of equations are used extensively in operations analysis, economics, psychology, and the sciences.