Equation solver

Solve linear and quadratic equations by entering coefficients a, b and c. Find real or complex roots and identify equations with no or infinitely many solutions.

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Set your data

Coefficient a of x²

Coefficient b of x

Constant c

Enter a, b and c for ax² + bx + c = 0. Supports quadratic and linear equations and complex roots; ℝ means infinitely many solutions and ∅ none. Finite coefficients from −10¹² to 10¹². Roots use 12 significant digits.

Result

Enter your data and run the tool. Your result will appear here.

Balance an equation

For linear equations, move through the steps. Applying the same operation to both sides keeps them equal.

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How to use the tool

For linear equations, move through the steps. Applying the same operation to both sides keeps them equal.

Fill in these fields: Coefficient a of x², Coefficient b of x, Constant c.
Select “Calculate” to obtain the result.
Enter a, b and c for ax² + bx + c = 0.
Supports quadratic and linear equations and complex roots; ℝ means infinitely many solutions and ∅ none.
Finite coefficients from −10¹² to 10¹².
Roots use 12 significant digits.

Method and principles

Δ > 0. Two distinct real roots.

Δ = 0. One repeated real root.

Δ < 0. Two complex conjugate roots.

Formula

a \times x^{2} + b \times x + c = 0

Practical example

Balance an equation

Input: $2 x - 8 = 0$
Result: $x = 4$

Calculation steps

Add 8 to both sides.
$0 + 8 = 8$
Divide both sides by 2.
$x = \frac{8}{2} = 4$
Substitute x into the original equation and check that the left side is zero.
$2 \times 4 - 8 = 0$

Input

Coefficient a of x²: 1
Coefficient b of x: -3
Constant c: 2

Result

x₁ = 2 x₂ = 1

Limits and checks

Limits and checks
Parameter	Value
Coefficient a of x²	≥ -1000000000000; ≤ 1000000000000
Coefficient b of x	≥ -1000000000000; ≤ 1000000000000
Constant c	≥ -1000000000000; ≤ 1000000000000

Equation solver

Set your data

Result

How to use the tool

Method and principles

Formula

Practical example

Balance an equation

Calculation steps

Limits and checks

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