Quadratic Equation Solver - Math Is Fun

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Quadratic Equation Solver

We can help you solve an equation of the form "ax2 + bx + c = 0" Enter your values of a, b and c here (details below):

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Quadratic Equations

It is a quadratic equation when it can be put in the form ax2 + bx + c = 0, and a is not zero:

Quadratic Equation

The name comes from "quad" meaning square, as the variable is squared (in other words x2).

These are all quadratic equations in different forms:

In disguise In standard form a, b and c
x2 = 3x -1 x2 - 3x + 1 = 0 a=1, b=-3, c=1
2(x2 - 2x) = 5 2x2 - 4x - 5 = 0 a=2, b=-4, c=-5
x(x-1) = 3 x2 - x - 3 = 0 a=1, b=-1, c=-3
5 + 1/x - 1/x2 = 0 5x2 + x - 1 = 0 a=5, b=1, c=-1

How Does this Work?

The solution(s) to a quadratic equation can be calculated using the Quadratic Formula:

x is [ -b plus minus square root of (b^2-4ac) ] / 2a

The "±" means we need to do a plus AND a minus, so there are normally TWO solutions !

The blue part (b2 - 4ac) is called the "discriminant", because it can "discriminate" between the possible types of answer:

  • when it is positive, we get two real solutions,
  • when it is zero we get only one solution,
  • when it is negative we get complex solutions

Learn more at Quadratic Equations

parabola

Real World

Many things follow the elegant path of a quadratic curve, such as balls, arrows and missiles.

They also have a lot of use in finding financial and engineering solutions.

Quadratic Equations Factoring Quadratics Completing the Square Graphing Quadratic Equations Real World Examples of Quadratic Equations Derivation of Quadratic Equation Algebra Index

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