What is Equation Solver?

The Equation Solver finds exact solutions for linear, quadratic, cubic, and higher-degree polynomial equations. Enter your equation in standard notation and get step-by-step solutions with real and complex roots.

Type the equation in standard math notation (use ^ for exponents, so x^2 = x squared) or switch to Coefficients mode and enter the numbers in front of each term. Quadratics get the discriminant calculation and full step-by-step working: the named quadratic formula x = (−b ± √(b² − 4ac)) / (2a), then b² − 4ac and the substitution. Cubics and quartics use numerical root-finding to return every real and complex solution. Results include the factored form like (x − 2)(x − 3), exact fraction roots such as 3/4 shown alongside the decimal, a number line marking the real roots (with multiplicity badges for repeated roots), and a function graph you can pan by setting your own X and Y bounds. Switch to Inequality mode to solve polynomial inequalities like x² − 5x + 6 < 0 and get the answer in interval notation on a shaded number line.

How to use

1. Type your equation (e.g., 2x² + 3x - 5 = 0) or select an equation type and enter the coefficients directly.
2. Click Solve to see all roots displayed with step-by-step working, including discriminant analysis for quadratics.
3. View the graph of the function with roots plotted, and copy the solution or export it as text.

When to use

• Homework help on quadratic and polynomial problems with shown working.
• Quick projectile motion or break-even calculations during physics or business work.
• Verifying your hand-solved roots before submitting an exam or assignment.

Result

A physics student enters 4.9t² - 20t + 15 = 0 to find when a projectile hits the ground, getting t = 0.97s and t = 3.12s with full quadratic formula steps shown.

FAQ

What's the difference between text mode and coefficients mode?

Text mode lets you paste an equation like 2x² + 3x − 5 = 0. Coefficients mode skips the parsing — you pick a degree and enter the numbers next to each term. Use coefficients if your equation has odd notation, like Greek letters or unusual variables.

Why does my quadratic return two complex roots instead of real ones?

The discriminant (b² − 4ac) is negative, so the parabola never crosses the x-axis. The solver still gives you the two complex roots in the form a ± bi. If you only need real solutions, the answer is 'none'.

How high a degree can the solver handle?

Up to degree 6 in either mode. Above degree 4 the solver switches to numerical methods (Durand–Kerner), so roots are accurate to about 10 decimal places rather than exact symbolic.

Why does the solver say 'invalid equation' when my input looks right?

Common causes: missing the = 0 on the right side, implicit multiplication like 2x instead of 2*x (this is supported but breaks if you write x2 meaning 2x), or mixing variable letters. Stick to a single variable (x or t).

Can I solve systems of equations or equations with two variables?

Yes — switch to the System tab to enter 2 or 3 linear equations in x, y, and z. The solver uses Gaussian elimination with partial pivoting and shows the back-substitution steps. For a single polynomial with x only, stay in Equation or Coefficients mode.

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