Algebra Calculator
Enter coefficients to solve ax + b = 0 or ax² + bx + c = 0, with the discriminant, roots and each step of the method.
Roots
x = 3 and x = 2
Discriminant 1
Discriminant
1
Vertex
(2.5, -0.25)
- Discriminant b² − 4ac
- 1
- √discriminant
- 1
- Root 1
- 3
- Root 2
- 2
- Sum of roots (−b/a)
- 5
- Product of roots (c/a)
- 6
How this was calculated
- 1.Identify a = 1, b = -5, c = 6.
- 2.Discriminant = b² − 4ac = -5² − 4 × 1 × 6 = 1.
- 3.x = (−b ± √disc) / 2a = (5 ± 1) / 2.
- 4.x₁ = 3 and x₂ = 2.
A positive discriminant gives two distinct real roots.
How the algebra calculation works
A linear equation has one solution: isolate x by moving the constant across and dividing by the coefficient.
A quadratic is solved with the quadratic formula, which is derived by completing the square. The discriminant (b² − 4ac) tells you how many real roots to expect before you calculate them.
A positive discriminant gives two real roots, zero gives one repeated root, and a negative discriminant gives a pair of complex conjugate roots.
Worked example
Solve x² − 5x + 6 = 0.
- →a = 1, b = −5, c = 6
- →Discriminant = 25 − 24 = 1
- →x = (5 ± 1) ÷ 2
Answer: x = 3 and x = 2.
Algebra FAQs
What if my equation has a different form?
Rearrange it into ax² + bx + c = 0 first, moving everything to one side. Then read off a, b and c.
What does a negative discriminant mean?
The parabola does not cross the x-axis, so there are no real solutions — only complex ones, which this tool shows with an i.
Can this solve simultaneous equations?
Not yet. This handles single linear and quadratic equations; substitution is usually quickest for pairs of simultaneous equations.
Algebra Calculator is part of the math calculators collection on Calcora, alongside 7 other tools. Results are calculated in your browser and are for information only — see our disclaimer.
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