Enter a supported form
For 2x + 3 = 7, select Linear and enter a = 2, b = 3, c = 7. For x² − 5x + 6 = 0, select Quadratic and enter 1, −5, 6. For a two-variable system, enter the first row’s a, b, c and the second row’s d, e, f in the displayed form.
Rearrange other equations into one of these forms first. Each coefficient accepts ordinary decimal notation with up to six decimal places and magnitude at most 1,000,000,000. Fractions, scientific notation and free-form equations are not accepted in coefficient boxes. Enter 0 rather than leaving a missing term blank.
Exact decisions and transparent results
Decimals are converted to equivalent integer coefficients. Linear equations and nonsingular linear systems return exact reduced fractions. Quadratic discriminants are calculated exactly: a negative discriminant means no real roots, zero means a repeated root, and positive means two real roots. If the square root of the discriminant is an integer, the roots are exact fractions; otherwise exact radical forms are retained beside approximate decimals.
Rational answers are checked by exact substitution. Irrational-root approximations use a 40-decimal-place integer square-root calculation before rounding to 12 significant digits. Their exact radical forms remain authoritative. Parentheses in a rational decimal mark repeating digits; any expansion that exceeds 60 digits without detected repetition is labelled truncated.
Handle degenerate equations correctly
A zero x² coefficient becomes a linear equation. An equation such as 0x + 2 = 2 holds for every real x, while 0x + 2 = 3 has no solution. For a two-variable system, a zero determinant is checked for inconsistency: the tool distinguishes parallel or contradictory equations from a shared solution line or unconstrained pair.
Keep and correct your work
All inputs, arithmetic and exports stay local. Changing a coefficient or equation type invalidates the previous result and preserves the other coefficient entries. Example and clear offer one Undo step that restores the complete form and any solved working; ordinary edits discard it. Downloads contain your entered form, answers and steps. No automatic storage, account or upload is used. Complex roots, nonlinear systems and higher-degree equations are outside this solver’s supported forms.