#### Explanation

Quadratic equations is also called as the second-degree algebraic expressions and defined in the form ax2 + bx + c = 0. The word quadratic is a derivative of quad, which stands for square. An "equation of degree 2" is another way to describe a quadratic equation. There are Numerous situations that can be solved using quadratic equations. You may be surprised to learn that a quadratic equation accurately predicts a rocket's trajectory after launch. A quadratic equation also has many uses in physics, engineering, astronomy, etc.
There are a maximum of two solutions for x in the quadratic equations (second-degree equations). These two solutions for x are referred to as the quadratic equations' roots and are given the designations (α, β).

An algebraic equation which have the second degree in x is called as quadratic equation. The quadratic equation is written in standard form as ax2 + bx + c = 0. This is the standard form used for quadratic equation, where x is the variable, Given a and b are the coefficients, and c is the constant term. The coefficient of x2 is 'a' which must be non-zero number means (a≠0) is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. Instead of using fractions or decimals, integral values are typically used to express the numerical values of a, b, and c.
The quadratic equations are also given in several ways in real-world math problems: for example. x3 = x(x2 + x - 3), -x2 = -3x + 1, (x - 1)(x + 2) = 0, 5x(x + 3) = 12x. The standard form of the quadratic equation must be applied to each of these equations before continuing.

Quadratic Equation: ax2 + bx + c = 0

#### How to solve Quadratic equation with a calculator?

• You need to enter coefficient a in the first input field "a".
• Then enter coefficient b in the first input field "b".
• Then enter coefficient c in the first input field "c".
• Click on submit, the results of "Quadratic Equation" will automatically appear below.

#### More Calculation (Examples of the standard form of a quadratic equation)

• Quadratic Equation Example 1: x² –x – 9 = 0
• a = 1
• b = -1
• c = -9
• Results = x = -2.5413812651491097, 3.5413812651491097
• Quadratic Equation Example 2: 5x² – 2x – 6 = 0
• a = 5
• b = -2
• c = -6
• Results = x = -0.9135528725660043, 1.3135528725660044
• Quadratic Equation Example 3: -x² +6x + 12 = 0
• a = -1
• b = 6
• c = 12
• Results = x = 7.58257569495584, -1.5825756949558398

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