Equation solver
Solve linear and quadratic equations, quartics in quadratic form, polynomial equations (rational roots by synthetic division), equations with fractions and systems of linear equations with up to 6 unknowns. The steps come from the calculation itself and every solution is checked by substituting it back.
The solutions and the steps will show up here.
How to use the equation solver
Type the equation with an equals sign and press "Solve". The unknown can be any letter. For a system, put each equation on its own line. You can use brackets, fractions (3x/2), powers (x^2) and decimals with a point (0.5x).
The steps aren't a template: they're the ones the algorithm actually follows. For a quadratic you see the discriminant and the quadratic formula. For a quartic in quadratic form (sometimes called biquadratic) you see the substitution t = x². For degree 3 or higher you see each root found with the rational root theorem and synthetic division, and for systems, every row operation of Gauss-Jordan elimination on the augmented matrix.
Examples worked out with this solver
- Quadratic equation:
- Quartic in quadratic form:
- System of linear equations (2×2):
To work with the coefficient matrix (determinant, inverse, rank) use the matrix calculator. If the equation comes from a word problem, the AI math solver sets it up for you from a photo. All the free calculators are in study tools.
Frequently asked questions
How do I type a system of equations?
One equation per line (or separate them with semicolons), for example x+y=3 on the first line and x-y=1 on the second. The solver picks out the unknowns, compares the rank of the coefficient matrix with the rank of the augmented matrix to tell whether the system is consistent, and solves it with Gauss-Jordan elimination. By hand you'd probably use substitution or elimination for a 2×2 system; the answer is the same, so you can use this to check your work.
What if a quadratic equation has no real solutions?
When the discriminant b² − 4ac is negative there are no real solutions. The solver tells you so and also shows the two complex solutions in case you need them.
Can I type decimals and fractions?
Yes: 0.5x+1.2=2.7 or x/2+6/5=27/10 both work. Use a point for decimals, since a comma between two digits isn't read as a decimal point. When a solution is rational it comes out as an exact fraction.
Does it solve exponential or trig equations?
Yes, numerically: it looks for the real solutions using sign changes and bisection. For trig equations it gives the solutions in [0, 2π) and writes them exactly when they're simple multiples of π (π/6, 5π/6). Exponential equations are searched between −20 and 20.
What about equations with x in the denominator?
The solver clears the fractions and solves the equation that's left. Then it throws out any solution that makes a denominator zero (an extraneous solution), because it isn't valid in the original equation.
