An equation says that two things are equal. The simplest are like 2 + 3 = 5. More interesting ones contain variables: 2x + 5 = 17. Solving the equation means finding the value of x that makes the statement true. Here, x = 6.

Equations can be linear, quadratic, polynomial, exponential, trigonometric, or differential. Each type has its own methods. The equals sign, introduced in the sixteenth century, turned mathematics into a symbolic language for stating and solving problems.

In applications, equations model relationships. Ohm's law, F = ma, and E = mc² are all equations. Solving them can be done by hand for simple cases, but complex systems require computers. The concept is fundamental to algebra and to all quantitative science.

• Statement of equality between expressions
• Solving means finding variable values
• Many types: linear, quadratic, differential
• Models relationships in science and engineering