Types of Equations and Examples
There are various types of equations, such as,


 Linear equation
 Equation with one variable
 Equation with two variables
 Equation with three variables
 Polynomial equation
 Monomial Equations
 Binomial Equation
 Trinomial Equation
 Quadratic equation
 Trigonometric equation
 Radical equation
 Exponential equation
 Rational equation
 Linear equation

1. Linear Equation:
A linear equation is an algebraic equation. In linear equation, each term is either a constant or the product of a constant and a single variable. If there are two variables, the graph of linear equation is a straight line.
General form of the linear equation with two variables is given below:
y = mx + c, m ≠ 0.
 Equation with one Variable: An equation who have only one variable, e.g.
 12x – 10 = 0
 12x = 10
 Equation with two Variables: An equation who have two variables, e.g.
 12x +10y – 10 = 0
 12x +23y = 20
 Equation with three Variables: An equation who have three variables, e.g.
 12x +10y 3z – 10 = 0
 12x +23y – 12z = 20
2.Polynomial Equation:
Polynomial Equation can be expressed in terms of monomial, binomial, trinomial and higher order polynomials. It may contain on both positive and negative values. Polynomials may also contains on decimal values.
Types of Polynomial Equations
 Monomial Equations
 Binomial Equations
 Trinomial Equations
Monomial Equations: The polynomial equations which has only one term is called as monomial equations. e.g.
12x = 0
2xy = 0
Binomial Equations: The polynomial equations which has two terms is called as binomial equations. e.g.
12x^{2} + 4y^{2 }= 0
27x^{2 }– 19 = 0
Trinomial Equations: The polynomial equations which has three terms is called as trinomial equations. e.g.
10xy + 23y – 2x = 0
3x^{3 }– 3 + 2x = 0
3. Quadratic Equation:
It is the second degree equation in which one variable contains the variable with an exponent of 2. Its general form is
ax^{2} + bx + c = 0, a ≠ 0
Examples of Quadratic Equations:
 x^{2} – 7x + 12 = 0
 2x^{2} – 5x – 12 = 0
4. Trigonometric equation:
These equations contains a trigonometric function. So, first we must have to introduce the trigonometric functions to explore them thoroughly. Only few simple trigonometric equations can be solved without any use of calculator but not at all. In some cases, inverse trigonometric functions are valuable.
5. Radical Equation:
It is an equation whose maximum exponent on the variable is 1/2 and have more than one term or a radical equation is an equation in which the variable is lying inside a radical symbol usually in a square root.
Examples of Radical equations:
x^{1/2} + 14^{ }= 0
(x+2)^{1/2} + y – 10
6. Exponential equation:
It is an equation who have variables in the place of exponents. This can be solved using the property: a^{x}=a^{y}=> x = y.
Examples of exponential euqations
 x^{a} = 0 Here “x” is base and “a” is exponent.
 10^{x} =0
 8^{a} = 64
7. Rational Equations:
A rational equation is one that involves rational expressions.
Example of Rational Equations:
x/4 = (x+12)/12
Read also: Types of Differential Equations