Equation Solver

Solve linear and quadratic equations and systems of two or three unknowns, with the steps shown.

Runs entirely in your browser. Nothing you type or paste is sent anywhere.

ax² + bx + c = 0

a

x² +

b

x +

c

= 0

Solving2x² − 4x − 6 = 0

Two real roots

Check: put the answer back in

1
Identify a, b and c
2x² − 4x − 6 = 0
a = 2, b = −4, c = −6
2
Work out the discriminant
Δ = b² − 4ac
Δ = (−4)² − 4 × 2 × (−6)
Δ = 16 + 48
Δ = 64
3
What the discriminant tells you
Δ is positive, so there are two different real roots. It is a perfect square, so they are rational (exact fractions).
4
Use the quadratic formula
x = (−b ± √Δ) / 2a
x = (4 ± √64) / 4
√64 = 8
5
The two roots
x₁ = (4 + 8) / 4 = 3
x₂ = (4 − 8) / 4 = −1
6
Vertex and axis of symmetry
h = −b / 2a = 4 / 4 = 1
k = a·h² + b·h + c = 2 × 1² + (−4) × 1 + (−6) = −8
The graph y = 2x² − 4x − 6 turns at (1, −8) and is symmetric about the line x = 1.

Type expressions with powers, roots, trigonometry, logs and constants, in degrees or radians, with a history.

Plot up to four functions of x, zoom and pan, and read exact values along each curve.

Mean, median, mode, standard deviation, quartiles and outliers from a list of numbers, with a histogram.

Add, multiply, transpose and invert matrices, with determinant, rank and row-reduced form.