A quadratic equation is a second-degree algebraic equation that can be expressed in the form:
$$ax^{2}+bx+c=0$$
where,
x— variable, unknown;
a, b, c— coefficients, constants, numbers.
The solution formula for the quadratic equation is:
$$x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$$
In the solution formula for the quadratic equation, the expression under the square root sign is called the discriminant:
$$D=b^{2}-4ac$$
A reduced quadratic equation is a quadratic equation with a coefficient of 1 for the quadratic term:
$$x^{2}+px+q=0$$
The solution formula for the reduced quadratic equation is:
$$x=-\frac{p}{2} \pm \sqrt{\left ( \frac{p}{2} \right )^{2}-q}$$