x = (−b ± √(b² − 4ac)) / 2a

For ax² + bx + c = 0

Example: x² − 5x + 6 = 0
a=1, b=−5, c=6
x = (5 ± √(25−24)) / 2 = (5 ± 1) / 2
x = 3 or x = 2

Discriminant b²−4ac > 0: two real roots · = 0: one root · < 0: no real roots

sin²θ + cos²θ = 1
tan θ = sin θ / cos θ

Double angle:
sin(2θ) = 2 sin θ cos θ
cos(2θ) = cos²θ − sin²θ

Pythagorean theorem:
a² + b² = c²

Work in radians for calculus; degrees for most geometry and physics problems.

log(ab)   = log(a) + log(b)
log(a/b)  = log(a) − log(b)
log(aⁿ)   = n × log(a)

Change of base:
logₐ(x) = log(x) / log(a)
        = ln(x) / ln(a)

log without base = log₁₀. ln = logₑ. Always the same rules, different bases.

A = P(1 + r/n)^(nt)

P = principal · r = annual rate
n = compounds/year · t = years

Continuous growth:
A = Pe^(rt)

Half-life:
t½ = ln(2) / λ  ≈  0.693 / λ

Use eˣ for continuous compounding, half-life, and radioactive decay.