Worked example
a: 1 b: -5 c: 6
→ x₁ = 3; x₂ = 2
Method and scope
Solve ax²+bx+c=0. Coefficients are scaled to reduce overflow; the stable q formula reduces cancellation. Δ is displayed relative to the squared scale. a=0 gives a linear equation; ∞ means identity, ∅ no solution.
Δ=b²−4ac; q=−½(b+sign(b)√Δ); x₁=q/a, x₂=c/q
Precision and limits
≈ marks an approximation. Display rounding does not change the internal calculation.