A quadratic equation is a type of polynomial equation that can be expressed in the standard form ax^2 + bx + c = 0 , where a , b , and c are constants, and a is not zero. The variable x represents an unknown value. Quadratic equations can have zero, one, or two solutions, which are the values of x that satisfy the equation. These equations are commonly solved using various methods, including factoring, completing the square, and the quadratic formula, which is x = \frac-b \pm \sqrt{b^2 - 4ac}2a . Quadratic equations are widely used in fields such as physics, engineering, and finance to model various real-world situations.