How to Calculate Quadratic Equation: A Step-by-Step Guide

Updated 5 Oct 2026 in Math & Geometry

Solves ax² + bx + c = 0.

These calculations come up in school, at work and in daily life, from PSLE and O-Level practice to measuring a room for new flooring. Doing them by hand builds understanding, and a calculator lets you check the answer instantly.

What you need

• a
• b
• c

Step by step

1. Enter the a.
2. Enter the b.
3. Enter the c.
4. The results update as you type, or press Calculate.
5. Read the roots first, then the supporting figures below it.

The formula

x = (−b ± √(b² − 4ac)) ÷ 2a.

Worked example

For example, with these inputs:

• a: 1
• b: -5
• c: 6

the calculator returns:

• Roots: x₁ = 3, x₂ = 2
• Discriminant: 1

A second example

Now change the inputs to:

• a: 1.25
• b: -5
• c: 6

the calculator returns:

• Roots: x = 2 ± 0.8944i (complex roots)
• Discriminant: -5

Practical tips

• Write down the formula before plugging numbers in; it prevents mixing up variables.
• For exam work, show your method; marks are often given for working, not just the answer.
• Keep units consistent: convert everything to the same unit before calculating.
• Round only at the final step to avoid accumulated rounding errors.

Background

A quick mental estimate before calculating is a powerful check. If a room's floor area comes out at 4,000 square metres or a percentage comes out above 100% when it should not, you know to look again.

Calculators are best used to check working rather than replace it, especially for exams where method marks count. Work the problem by hand first, then confirm with the calculator.

These calculations appear throughout the Singapore syllabus, from primary school percentages and fractions to secondary school algebra and geometry. Understanding the formula makes problem sums easier because you can recognise which quantity is missing.

Related calculations

• Perimeter of a Triangle Calculator: Calculates the perimeter of a triangle from the measurements you enter.
• Perimeter of an Ellipse Calculator: Calculates the perimeter of an ellipse from the measurements you enter.
• Arc Length Calculator: Calculates the arc length from the measurements you enter.
• Volume of a Cube Calculator: Calculates the volume of a cube from the measurements you enter.

Want to skip the arithmetic? The free Quadratic Equation Solver does all of this instantly and updates as you type.

Run your own numbers: Quadratic Equation Solver