Quadratic Equation Solver
Solve a quadratic equation and see the roots, the discriminant, and the working, with the formula explained.
Solving the classic equation
A quadratic equation is one where the highest power is a square — of the form a times x squared, plus b times x, plus c, equal to zero. Solving it means finding the values of x that make it true, its roots. This solves any quadratic and shows the roots and the working.
The quadratic formula
The reliable way to solve any quadratic is the quadratic formula, which gives the roots from the three coefficients a, b and c:
x = ( -b (plus or minus) the square root of (b squared - 4ac) ) / 2aThe part under the square root, b squared minus four a c, is called the discriminant, and it tells you the nature of the solutions before you even finish: if it is positive there are two real roots, if zero there is one repeated root, and if negative there are no real roots (the solutions are complex).
Worked example
Take x squared minus 5x plus 6 = 0, so a is 1, b is minus 5, c is 6:
Quadratics are not just an exam staple — they describe the path of a thrown ball, the shape of a satellite dish, and countless relationships in physics and engineering where something curves. Seeing the discriminant and the working, rather than just the answer, is what makes the method something you can apply yourself rather than a black box.
Quadratic Equation Solver FAQ
What is the quadratic formula?
x equals negative b, plus or minus the square root of b squared minus four a c, all over two a. It solves any quadratic from its coefficients.
What does the discriminant tell me?
The part under the square root: if positive there are two real roots, if zero one repeated root, and if negative no real roots — so it reveals the nature of the solutions.
Why do quadratics matter beyond class?
They describe curved relationships everywhere — the path of a thrown ball, the shape of a dish, and many physics and engineering relationships.
Is anything uploaded?
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