Quadratic Formula Calculator

Use this quadratic formula calculator to solve ax² + bx + c = 0. It shows clear steps and a final answer for every case.

How This Tool Works

The calculator uses the quadratic formula x equals negative b plus or minus the square root of b squared minus 4ac, all over 2a. You enter a, b, and c. The tool builds your equation, computes the discriminant, and then finds the roots.

You also see a full step-by-step solution. It labels each step, from your equation to the final answer. Results display to four decimal places when needed.

• Step 1 shows your equation with your numbers.
• Step 2 lists a, b, and c.
• Step 3 finds the discriminant, often written as Delta.
• Step 4 applies the formula and computes the roots.
• A final box states the case and the solutions.

Delta greater than zero gives two real roots. Delta equal to zero gives one repeated root. Delta less than zero gives two complex roots that use i for the square root of negative one.

Step-by-Step Guide

Step 1: Fill in the Coefficients

Enter the values for a, b, and c from your equation ax² + bx + c = 0.

• a is the number in front of x². Use a nonzero value for a.
• b is the number in front of x.
• c is the constant term.
• Use whole numbers or decimals only.

Example for x² + 5x + 6 = 0. Set a to 1. Set b to 5. Set c to 6.

Step 2: Hit Calculate

Click the Calculate Roots button to run the math. The result also updates as you type new values.

Step 3: Read the Results

Look for the labeled steps and the final answer box. Here is how to read each case.

• Two real roots: You see x1 and x2 as two different real numbers.
• One repeated root: You see a single value for x, repeated.
• Two complex roots: You see a real part and an imaginary part with i.

These roots solve ax² + bx + c = 0. For real roots, they mark x intercepts on the graph of y equals ax² + bx + c.

Why Choose Our Calculator?

This quadratic formula calculator gives fast results with clear steps. Students, teachers, and professionals can confirm work in seconds.

• Homework checks for algebra and precalculus.
• Quick validation during study or exam prep.
• Factor checks by reading roots and building factors.
• Physics and engineering problems that reduce to a quadratic.
• Graph checks for x intercepts and solution counts.
• Coding tests that need correct numeric roots.

You get an instant walkthrough that matches standard classroom methods. That helps you learn the process while you solve.

A Quick Look at the Code

No code needed on your end, just numbers. Here is what happens behind the scenes.

• The tool reads a, b, and c as numbers.
• It stops and shows a clear message if a, b, or c is not a number.
• It also checks that a has a value other than zero.
• It builds your equation and lists your coefficients.
• It computes the discriminant b squared minus 4ac.
• It calculates roots based on the sign of the discriminant.
• It formats each number to as many as four decimals.
• It shows a final answer box with the case and solutions.

Notes and limits to keep in mind:

• Use decimal form for fractions, write 0.5 instead of 1 slash 2.
• Very large or tiny inputs can produce small rounding differences.
• The solver returns numeric roots rather than a factorized form.
• Complex roots appear as a real part plus or minus a number times i.
• You can press Calculate Roots or just change a field to refresh the result.

Final Thoughts

This quadratic formula calculator keeps the math clean and the steps clear. Enter your numbers, check the steps, and read the answer with confidence. Try a few examples and make this tool part of your study kit.