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Active Formula: x = (-b ± √(b² - 4ac)) / (2a)
Result: x₁ = 5, x₂ = 2
  1. Equation Form: 1x² - 7x + 10 = 0
  2. Discriminant (D = b² - 4ac): (-7)² - 4(1)(10) = 49 - 40 = 9 (D > 0, Two Real Roots)
  3. Square Root of Discriminant: √9 = 3
  4. Roots Calculation: x = (7 ± 3) / 2 → x₁ = 10 / 2 = 5, x₂ = 4 / 2 = 2
FORMULA DIRECTORY

Core Mathematical Formulas Reference

Quick lookup directory for essential formulas across Algebra, Geometry, and Calculus.

ALGEBRA

Algebraic Identities

Quadratic Formula x = (-b ± √(b² - 4ac)) / 2a
Difference of Squares a² - b² = (a - b)(a + b)
Binomial Expansion (a ± b)² = a² ± 2ab + b²
Slope-Intercept Form y = mx + b
GEOMETRY

Geometric Equations

Area of a Circle A = πr²
Circumference of a Circle C = 2πr
Area of a Triangle A = ½ × base × height
Pythagorean Theorem a² + b² = c²
CALCULUS

Calculus Rules

Power Rule (Derivatives) d/dx(xⁿ) = n·xⁿˉ¹
Product Rule (uv)' = u'v + uv'
Quotient Rule (u/v)' = (u'v - uv') / v²
Power Rule (Integrals) ∫ xⁿ dx = (xⁿ+¹) / (n + 1) + C
STUDY GUIDES & TUTORIALS

Essential Formula Step-by-Step Guides

Procedural walkthroughs and worked examples showing how to apply essential formulas accurately.

Algebra 5 Min Read

How to Use the Quadratic Formula Step-by-Step

A procedural walkthrough calculating the discriminant, detecting real roots, and avoiding sign mistakes.

Read Guide →
Geometry 6 Min Read

Slope-Intercept Form Explained

Understand linear functions (y = mx + b), vertical intercepts, rate of change, and coordinate line plotting.

Read Guide →
Calculus 5 Min Read

How to Use the Power Rule for Derivatives

Master polynomial differentiation, negative exponents, and tangent slope derivation with verified examples.

Read Guide →
FAQ

Frequently Asked Questions

Understanding the mathematical principles and derivation behind a formula enables you to apply it across non-standard real-world problems and avoids sign or substitution errors.
When the discriminant (b² - 4ac) equals zero, the quadratic equation possesses exactly one repeated real root (x = -b / 2a), meaning the parabola touches the x-axis at a single vertex point.
No, the classic formula (a² + b² = c²) strictly applies to right-angled triangles with a 90-degree angle. For acute or obtuse triangles, use the Law of Cosines (c² = a² + b² - 2ab·cos(C)).
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