Formal Sciences

Mathematics

~628 CE

Beginner

Quadratic Formula

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Solves any quadratic equation ax² + bx + c = 0 by finding its roots.

By Brahmagupta, Al-Khwarizmi

Formal Sciences

Quadratic Formula

~628 CE · Brahmagupta

Human Reviewed

84%

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Story PortalWho discovered this?Discover how Brahmagupta and others shaped this equation.Visual PortalWhat does it look like?See the equation come alive in the Visual Studio.Machine PortalWhere is it used?Explore machines powered by this equation — projectile motion.Math PortalWhat does it derive from?Trace the mathematical lineage from pythagorean theorem.Future PortalWhere is it going?Automated theorem proving

Why it matters: Enabled systematic solution of parabolic motion, optimization, and engineering design problems.

Discoverers: Brahmagupta, Al-Khwarizmi (~628 CE)

What does it mean?

Solves any quadratic equation ax² + bx + c = 0 by finding its roots.

Why should I care?

Enabled systematic solution of parabolic motion, optimization, and engineering design problems.

Equation Compass

North — Prerequisites

West — History

East — Applications

South — Derivations

Derivation

Variables & Units

Symbol	Name	Unit	Meaning
$a$	Coefficient	—	Leading coefficient of x²
$b$	Coefficient	—	Coefficient of x
$c$	Constant	—	Constant term
$x$	Root	—	Solution value

Worked Example

For x² - 5x + 6 = 0: x = (5 ± √(25-24))/2 = 3 or 2.

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Sources & further reading

Search Wikipedia Search Wolfram MathWorld Open in Wolfram|Alpha Watch explainers on YouTube

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