**What is the Equation?**

An equation is a mathematical statement that two things are equal. It consists of two expressions, one on each side of an ‘equals’ sign

**For Example:**

8 + 2 = 10

This equation states that 10 is equal to the sum of 8 and 2, which is for sure, true. In an equation, the left-hand side is always equal to the right-hand side.

**Equations containing Variables**

The most usual equations consist of one or more variables. If we suppose x stands for an unknown number and write down the equation as:

X=11+4

As we know, the left hand side and right hand side of equations are equal, so we can say that **x** must be 11+4 or 15. This is the only answer that x can have or that makes the equation a true statement. We can say that **x=15** ‘satisfies’ the above equation.

The process of calculating the values for the unknowns is known as “solving the equations”. We usually say that we “solve for value of x” – means solving the equations to find the value of the unknown value x.

**A habitual mistake**

You usually look at things that are called as equations but actually, they are not the equations.

**For example:**

You can see something like this and referred to as an equation:

X^{3}−2x^{2}+4

This statement does not have an equal sign in it, and that is why this is not an equation. This statement is called as an ‘expression’.

**Algebraic Equations**

Equations often contain algebra. Algebra is used in maths when you do not know the exact number in a calculation.

These are the combination of polynomials, equal sign, and constant values.

**For Example:**

4x^{2}+ 5x + 2 = 0

**Different types of equations in mathematics**

Following are the types of equations on the basis of the power of variables

**Linear equations**

Linear means having one line. In these equations, the highest degree of the variable is 1. These are equations of the type

E= ax+b

where ‘a’ and ‘b’ are real numbers and ‘x’ is a variable that cannot be equal to zero. In this equation, ‘x’ has exponent equal to 1.

**Example**

E= 5x+6, E= x+4

These are linear equations.

**Quadratic equations**

These are the equations that contain maximum power or exponent of variable equals to 2. These are the equations of the type

ax^{2}+bx+c= 0

where ‘a’ and ‘b’ are real numbers and ‘x’ is a variable that cannot be equal to zero.

**Example:**

4x^{2}+ 5x + 6 = 0

3x^{2}+ 2x + 8 = 0

These are quadratic equations.

**Radical equations**

These are equations whose maximum power on the variable is 1/2 and have more than one term. Here we use the radical symbol and the variable is lying inside a radical symbol usually we say that in a square root.

**Example:**

These are radical equations.

**Polynomial equations**

A polynomial equation is the one that takes away the limit of the highest exponent of variables. The equation consists of several terms and raised to any power of the variable.

**Example:**

4x5 + 3x3 + 6x2 + 8x + 15 9x9 + 8x7 + x3 + 4x + 20

These are the polynomial Equations.

**Some other types of Equations**

**Exponential equations**

These are the equations that contain variables in the place of exponents.

**Example:**

45^{x}= 5

2^{y }= 10

These are Exponential Equations.

**Trigonometric equations**

These are equations in which the variables are affected by trigonometric functions.

cosx + 1 = + 5 tanx + 10 = 15

These are the trigonometric Equations.

**Uses of Equations in real life**

Many professionals use equations every day, including air traffic controllers, architects, computer programmers, and carpenters. Engineers, architects, and video-game designers all use equations in their work too.