What type of quadratic equation cannot be solved using the quadratic formula?

All quadratic equations can be solved using the quadratic formula, which is applicable to any equation in the standard form ( ax^2 + bx + c = 0 ), where ( a \neq 0 ). However, if the equation does not fit this standard form—such as if it is not a polynomial, if it contains non-numeric coefficients, or if it is missing the ( x^2 ) term (making it linear instead)—then it cannot be solved using the quadratic formula.