root formula for a quadratic equation of one variable

symbols, variables and units

a, b, c: polynomial coefficients; x: unknown quantity; the dimensions should make all items consistent.

applicable conditions and boundaries

a≠0; the real number range requires b²−4ac≥0, and the complex number range always has roots.

formula source code

The following is a copyable LaTeX expression.

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Reference and Extended Learning

is organized according to model definition and assumptions. Please check actual conditions and original literature before engineering, research and clinical use.