Quadratic Formula
x = (-b ± √(b² - 4ac)) / 2a
Solve quadratic equations of the form ax² + bx + c = 0
Slope Formula
m = (y₂ - y₁)/(x₂ - x₁)
Calculate the slope between two points
Simultaneous Equations Solver
a₁x + b₁y = c₁ ; a₂x + b₂y = c₂
Solve a pair of linear equations in two variables
Arithmetic Progression - nth Term
aₙ = a + (n - 1)d
Find the nth term of an arithmetic progression
Arithmetic Progression - Sum
Sₙ = n/2 × [2a + (n - 1)d]
Find the sum of the first n terms of an arithmetic progression
Geometric Progression - nth Term
aₙ = a × r⁽ⁿ⁻¹⁾
Find the nth term of a geometric progression
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Geometric Progression - Sum
Sₙ = a(rⁿ - 1) / (r - 1)
Find the sum of the first n terms of a geometric progression
Logarithm
log_b(x) = y means b^y = x
Calculate logarithm base 10
Exponential Function
f(x) = a × b^x
Calculate exponential function value
Linear Equation Solver
ax + b = c → x = (c - b) ÷ a
Solve linear equations in the form ax + b = c
Cubic Equation Solver
ax³ + bx² + cx + d = 0
All roots (real and complex) of a cubic equation, using the trigonometric/Cardano method. The result shown is the largest real root
Logarithm Calculator (Any Base)
log_b(x) = ln(x) ÷ ln(b)
Logarithm of a number to any base using the change-of-base rule
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