Quadratic Formula Calculator

Solve quadratic equations quickly and accurately with our powerful calculator. Whether you're a student, teacher, or professional, our tool makes complex math simple.

What is a Quadratic Equation?

A quadratic equation is a second-degree polynomial equation in a single variable x. It's generally written in the standard form ax² + bx + c = 0, where a, b, and c are constants, and a ≠ 0. These equations are fundamental in algebra and have numerous real-world applications in physics, engineering, and economics.

How to Use Our Quadratic Formula Calculator

  1. Enter the coefficients a, b, and c from your quadratic equation (ax² + bx + c = 0).
  2. Click the "Calculate" button to see the results.
  3. Review the step-by-step solution, including the discriminant calculation and root determination.
  4. Examine the graph to visualize your quadratic function.

Our calculator handles all types of quadratic equations, including those with real roots, one repeated root, or complex roots. It's an invaluable tool for students learning algebra, professionals solving engineering problems, or anyone needing quick and accurate quadratic equation solutions.

Step 1: Understand the Quadratic Equation

A quadratic equation has the general form:

ax² + bx + c = 0

Where:

  • a ≠ 0
  • a, b, and c are constants
  • x is the variable

Step 2: Identify the Coefficients

Look at your equation and identify the values for a, b, and c.

Example: For the equation x² - 5x + 6 = 0
  • a = 1
  • b = -5
  • c = 6

Step 3: Enter the Coefficients

Enter the values of a, b, and c into the calculator's input fields.

Step 4: Calculate and Interpret Results

Click the "Calculate" button and interpret the results:

  • Two real roots: The equation crosses the x-axis at two points.
  • One real root: The equation touches the x-axis at one point (tangent).
  • Two complex roots: The equation doesn't cross the x-axis.

Examples

Example 1: Two Real Roots

Equation: x² - 5x + 6 = 0

  • a = 1, b = -5, c = 6
  • Result: x₁ = 3, x₂ = 2

The parabola crosses the x-axis at x = 3 and x = 2.

Example 2: One Real Root

Equation: x² - 4x + 4 = 0

  • a = 1, b = -4, c = 4
  • Result: x = 2

The parabola touches the x-axis at x = 2.

Example 3: Two Complex Roots

Equation: x² + x + 1 = 0

  • a = 1, b = 1, c = 1
  • Result: x₁ = -0.5 + 0.87i, x₂ = -0.5 - 0.87i

The parabola doesn't cross the x-axis.