Free Quadratic Formula Calculator (Step-by-Step Solver)

Quadratic Equation Solver
ax² + bx + c = 0

Enter values (fractions like 1/4 are supported) and hit calculate.

a =
b =
c =

Quadratic Formula Calculator with Steps

Are you struggling with algebra homework or complex math equations? Our free quadratic formula calculator is designed to solve any standard quadratic equation instantly. Whether you are dealing with whole numbers, decimals, or fractions, this quadratic equation formula calculator provides the exact roots (x-intercepts) alongside a complete, step-by-step breakdown of the math.

Unlike standard calculators that just spit out a final decimal, our tool shows you exactly how the answer was found, making it the perfect study companion for algebra students.

How to Do Quadratic Formula on Calculator

Wondering how to do quadratic formula on calculator tools like ours? It is incredibly simple:

  1. Identify your values: Ensure your equation is in the standard form: ax^2 + bx + c = 0. Identify your a, b, and c values.
  2. Enter the inputs: Type your values into the corresponding boxes above. You can enter whole numbers, decimals, or even fractions (like 1/4 or -3/2).
  3. Click Calculate: Hit the calculate button.
  4. View your steps: The tool will instantly generate the optimal quadratic formula for calculator display, showing you the discriminant, the simplified root fractions, and the final real or imaginary solutions.

How to Calculate Quadratic Formula (The Math Explained)

Quadratic Equation
ax² + bx + c = 0
x =
-b ± √ b² – 4ac
2a

👆 Tap parts of the formula to learn more.

This is the standard form of a quadratic equation, where x represents the unknown variable. The coefficients a, b, and c are known numbers, and the coefficient ‘a’ cannot be zero.

This symbol indicates that you must calculate the equation twice: once adding the square root, and once subtracting it. This is why quadratic equations typically have two solutions (roots).

The expression under the square root is called the discriminant. It tells you the nature of the roots:

  • Positive: 2 real roots
  • Zero: 1 real root
  • Negative: 2 imaginary roots

You must divide the entire top half of the equation by 2 times the ‘a’ coefficient. Remember to calculate the entire top numerator first before dividing!

If you want to know how to calculate quadratic formula problems by hand, you must use the standard equation:

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Our calculator automates this exact process. Here is how it works under the hood:

Imaginary/Complex Roots: If the discriminant is a negative number, the equation does not cross the x-axis. Our calculator flawlessly handles this by introducing the imaginary unit (i).

The Discriminant (Delta Δ): First, the tool calculates the part under the square root, known as the discriminant (b^2 - 4ac).

Two Real Roots: If the discriminant is greater than zero, the parabola crosses the x-axis twice, giving you two distinct real answers.

One Real Root: If the discriminant is exactly zero, the vertex of the parabola touches the x-axis, resulting in one single real answer.

Frequently Asked Questions

If you are wondering how to put quadratic formula in calculator TI 84 Plus (or the TI-84 Plus CE), you have a few options. The easiest way is to use the built-in PolySmlt2 app by pressing the [APPS] button and selecting "Polynomial Root Finder."

Alternatively, to program it yourself, press [PRGM], tab over to NEW, name it "QUAD", and use the Prompt A, B, C commands followed by the formula. However, if you need to see the step-by-step working for your homework, using our free web calculator is much faster!

Yes! While the Mathway quadratic formula calculator is a great tool, it often hides the step-by-step solving process behind a premium subscription paywall. Our calculator is 100% free and shows you the exact fraction breakdowns, discriminant math, and complex roots without requiring you to create an account.

Absolutely. Unlike many basic calculators, you can type fractions directly into the $a$, $b$, and $c$ input boxes (for example, 3/4 or -1/2). The calculator will automatically parse the fraction and give you accurate mathematical results.

In the standard format ax^2 + bx + c = 0, the a value cannot be zero. If a = 0, the x^2 term disappears, and it becomes a linear equation (bx + c = 0). Our calculator is smart enough to detect this and will automatically solve it as a linear equation for you!