Formula Library

Comprehensive collection of mathematical, physical and chemical formulas

Mathematics
45 formulas
Physics
32 formulas
Chemistry
28 formulas
Algebra
18 formulas
Calculus
15 formulas
Geometry
12 formulas

Quadratic Formula

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Description
The quadratic formula provides the solution(s) to a quadratic equation of the form \(ax^2 + bx + c = 0\), where \(a\), \(b\), and \(c\) are coefficients. The expression under the square root, \(b^2 - 4ac\), is called the discriminant and determines the nature of the roots.
Variables
Symbol Description
\(a\) Coefficient of \(x^2\)
\(b\) Coefficient of \(x\)
\(c\) Constant term
\(x\) Variable to solve for
Applications
  • Solving quadratic equations
  • Finding roots of polynomials
  • Physics problems involving motion
  • Engineering calculations
  • Economics and finance models
Example

Solve the equation: \(2x^2 + 4x - 6 = 0\)

Solution:

Here, \(a = 2\), \(b = 4\), \(c = -6\)

Discriminant: \(d = b^2 - 4ac = 4^2 - 4(2)(-6) = 16 + 48 = 64\)

Roots: \(x = \frac{-4 \pm \sqrt{64}}{4} = \frac{-4 \pm 8}{4}\)

First root: \(x_1 = \frac{-4 + 8}{4} = \frac{4}{4} = 1\)

Second root: \(x_2 = \frac{-4 - 8}{4} = \frac{-12}{4} = -3\)

Related Formulas
Why Learn Formulas?

Formulas are the building blocks of mathematics and science. They provide concise representations of relationships between quantities and enable us to solve complex problems efficiently.

Key benefits of understanding formulas:

Tips for mastering formulas:

  1. Understand the derivation and assumptions behind each formula
  2. Learn the meaning and units of each variable
  3. Practice applying formulas to different problems
  4. Create flashcards for quick review
  5. Relate formulas to real-world applications

Popular Formulas

Pythagorean Theorem
Geometry
\(a^2 + b^2 = c^2\)
Relates the sides of a right triangle
Newton's Second Law
Physics
\(F = ma\)
Force equals mass times acceleration
Quadratic Formula
Algebra
\(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
Solves quadratic equations
Ideal Gas Law
Chemistry
\(PV = nRT\)
Relates pressure, volume and temperature

Recently Added

Euler's Formula
Mathematics
\(e^{i\pi} + 1 = 0\)
Connects exponential and trigonometric functions
Maxwell's Equations
Physics
\(\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}\)
Fundamental equations of electromagnetism

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