QuadSolve

Quadratic Formula Calculator

x = (−b ± √(b²−4ac)) / (2a).

The discriminant decides the outcome

The value under the square root (b² − 4ac) tells you what kind of roots to expect: positive means two real roots, zero means one repeated root, and negative means two complex roots.

Real-world quadratics

Anything involving projectile motion, the shape of a satellite dish, or maximizing area/profit under a constraint tends to produce a quadratic equation — this formula solves all of them exactly.

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QuadSolve

Quadratic Formula Calculator

x = (−b ± √(b²−4ac)) / (2a).

Discriminant

x = (−b ± √(b²−4ac)) / (2a)

Roots: 4, -1

What you entered

a: 1b: -3c: -4

1
Discriminant
-3² − 4×1×-4= 25
2
Two real roots
x = (−-3 ± √25) ÷ (2×1)= 4, -1

Result

Discriminant: 25

For 1x² + -3x + -4 = 0, the discriminant is 25, giving roots 4, -1.

The discriminant decides the outcome

The value under the square root (b² − 4ac) tells you what kind of roots to expect: positive means two real roots, zero means one repeated root, and negative means two complex roots.

Real-world quadratics

Anything involving projectile motion, the shape of a satellite dish, or maximizing area/profit under a constraint tends to produce a quadratic equation — this formula solves all of them exactly.