Equations Calculator
Linear Equation Calculator
Enter the coefficients of ax + b = 0 and get the solution x = −b/a instantly, with the for...
Read MoreQuadratic Equation Calculator
Enter a, b and c of ax² + bx + c = 0 to get the discriminant and both roots, real, repeate...
Read MoreCubic Equation Calculator
Enter a, b, c and d of ax³ + bx² + cx + d = 0 to get all roots, including the complex pair...
Read MoreAbout This Category
Linear, quadratic and cubic equations, solved rather than approximated. Each page reports the roots and says when they are complex, which is the case a graph hides.
The quadratic page uses the discriminant to decide the case before solving: positive gives two real roots, zero a double root, negative a conjugate pair. The cubic page falls back to trigonometry when all three roots are real, because Cardano’s formula becomes numerically unstable there.
Frequently Asked Questions
What does a negative discriminant mean?
The parabola does not cross the x-axis, so the solutions are complex. They always come as a conjugate pair, a + bi and a − bi.
How many roots does a cubic have?
Three, counted with multiplicity, and at least one is always real. That real root can be found first, after which the rest are a quadratic.
Why do the roots sometimes look slightly off?
Floating-point arithmetic. Values are shown rounded; substituting them back can miss zero by a small amount that is not a calculation error.