Calculator
What the Algebra Solver does
Algebra Solver: calculates Solution / Root 1, Root 2 (quadratic only) and Discriminant b²−4ac (quadratic only) from Equation Type, a (in ax + b = c) and b. Example: equation type Linear (ax + b = c), a (in ax + b = c) 2 and b 3 gives solution / root 1 4.
From Equation Type, a (in ax + b = c), b and c, this tool derives Solution / Root 1, Root 2 (quadratic only) and Discriminant b²−4ac (quadratic only). You can nudge a single number and watch the effect straight away.
Most people who open the Algebra Solver are people who want the working shown. Checking a result a second way is the cheapest way to catch an arithmetic slip.
There is no account, no upload and no server round trip, because the page does the work itself.
The method, a field-by-field reference and a worked example built from the defaults are all on this page.
What do the Algebra Solver fields mean?
The Algebra Solver uses 7 inputs. Pre-filled inputs double as documentation: each one shows what a reasonable value looks like.
| Field | What to enter | Default |
|---|---|---|
| Equation Type | choose from Linear (ax + b = c) or Quadratic (ax² + bx + c = 0) | Linear (ax + b = c) |
| a (in ax + b = c) | required | 2 |
| b | required | 3 |
| c | required | 11 |
| a (x² coeff) | required | 1 |
| b (x coeff) | required | -5 |
| c (constant) | required | 6 |
How does the Algebra Solver work?
Each output is derived from the inputs above in a single pass; there is no hidden state carried between runs, so the same inputs always give the same calculation.
Values are checked first: an out-of-range or non-numeric entry names the offending field instead of returning nonsense.
Worked example
These are the values the Algebra Solver loads by default, and the result it produces from them. This is the worked example the page starts from, reproduced here so you can check the arithmetic.
| Equation Type | Linear (ax + b = c) |
|---|---|
| a (in ax + b = c) | 2 |
| b | 3 |
| c | 11 |
| a (x² coeff) | 1 |
| b (x coeff) | -5 |
| c (constant) | 6 |
| Solution / Root 1 | 4 |
|---|---|
| What this means | x = (c − b) / a = 4 |
Beyond the formula: solving a linear equation for x
Solving ax+b=c for x has exactly one solution whenever a is nonzero. A linear equation with no solution, or infinitely many, only arises when a itself is zero, which this calculator correctly refuses to divide by rather than guessing.
Common mistakes and sanity checks
- If a = 0, the equation collapses to "b = c", which is either always true (infinitely many solutions, when b already equals c) or always false (no solution), neither case is a value of x, which is why division by zero is barred here rather than silently producing an answer.
- A quick way to check any linear solution by hand: substitute x back into the original ax+b and confirm it equals c. That catches sign errors, the most common mistake when rearranging equations manually.
- Real-world "solve for x" problems (unit conversions, break-even points, mixture problems) almost always reduce to exactly this form once simplified, even when they don’t look linear at first glance.
How to use it
- Pick a value for Equation Type: the options are Linear (ax + b = c) or Quadratic (ax² + bx + c = 0).
- Type a (in ax + b = c).
- Enter b.
- Set c.
- Put a (x² coeff).
- Key in b (x coeff).
- Fill in c (constant).
- Watch the results panel as you type: it recalculates on every keystroke.
- The panel reports Solution / Root 1, Root 2 (quadratic only), Discriminant b²−4ac (quadratic only) and What this means.
- Copy Link puts the current inputs in the URL, so bookmarking it brings the same numbers back.
What this tool does not do
- Displayed values are rounded; the underlying calculation keeps full precision.
- Very large or very small numbers hit JavaScript floating-point limits (about 15 significant digits).
- Assumptions built into the method are stated above, but they are still assumptions.
Frequently asked questions
You need Equation Type, a (in ax + b = c), b, c, a (x² coeff), b (x coeff) and c (constant). Every box already holds a working value, which makes it easy to isolate the effect of a single variable.
With the values loaded when the page opens, solution / root 1 comes out as 4. The figure is derived from the inputs above, so it updates whenever they do.
No record is kept. We never receive what you type, so there is nothing on our side to retain.
No. There is no account, no usage cap and no trial period. The site is funded by advertising rather than by charging for the tools.
The calculation is exact for the method described above. Where a value is rounded for display, the underlying figure keeps full precision.