How To Solve a Quadratic Equation

Example


=(-C12+SQRT(C12^2-4*B12*D12))/(2*B12)

Download Example File

Generic Formula

There are two possible solutions for any quadratic equation. This is one possible solution.


=(-B+SQRT(B^2-4*A*C))/(2*A)

This is the other possible solution.


=(-B-SQRT(B^2-4*A*C))/(2*A)

A – This is the coefficient of the squared term in the quadratic equation.
B – This is the coefficient of the single powered term in the quadratic equation.
C – This is the constant in the quadratic equation.

What It Does

These formulas will give the solutions to a quadratic equation of the form Ax^2 + Bx + C = 0.

How It Works

This is a simple algebraic formula and uses the SQRT function which returns the square root of a given number and the ^ operator which raises a given number to a given power.

In our example x^2 – 3x + 2 = 0 the solution is given by =(-(-3)+SQRT(-3^2-4*1*2))/(2*1) which results in 2. Similarly the other solution is 1.

Not every quadratic equation has a solution in the real numbers, when this is the case the formula will result in a #NUM! error.

About the Author

John MacDougall

John is a Microsoft MVP and qualified actuary with over 15 years of experience. He has worked in a variety of industries, including insurance, ad tech, and most recently Power Platform consulting. He is a keen problem solver and has a passion for using technology to make businesses more efficient.