How To Solve a Quadratic Equation

2017-12-24

Example

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

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 MacDougall

John is a Microsoft MVP and freelance consultant and trainer specializing in Excel, Power BI, Power Automate, Power Apps and SharePoint. You can find other interesting articles from John on his blog or YouTube channel.

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