Quadratic equations can be solved by using any one of the following methodologies: factoring, completing the square, graphing, Newton’s method, and using the quadratic formula. Our quadratic equation solver uses the quadratic formula to find all possible solutions any equation in the form of ax2 + bx + c = 0.

To use this quadratic equation calculator, simply enter the values for the three variables a, b, and c, and click Calculate. After running your calculation, you will be presented with Solution 1, Solution 2, and the equation discriminant.

In algebra, a quadratic equation is an algebraic polynomial equation. The word quadratic is derived from the Latin word quadrates, which means square. The history of solving quadratic equations dates as far back as the Babylonian’s in 2000 BC. However, the actual quadratic formula wasn’t discovered until far later in time. The evolution of the quadratic formula passed through the minds and hands of several notable and brilliant mathematicians including: Euclid of Alexandria, Pythagoras of Samos, Diophantus of Alexandria, Muhammad ibn Musa al-Khwarizmi, Abraham bar Hiyya Ha-Nasi , Yang Hui, and Gerolamo Cardano. Lastly, René Descartes was the first to publish the quadratic formula, in the form we that know today, in the year 1637.

The three variables required to solve an equation with the quadratic formula are known as constants and they are represented by the letters a, b, and c. The variable a is called the quadratic coefficient, the variable b is called the linear coefficient, and the variable c is called the constant term. The quadratic formula can be seen in the box below.

x = ( -b ± sqrt(b2 – 4ac) ) / 2a

The expression featured underneath the square root sign is called the discriminant and it is often represented by the Greek upper case delta (Δ). The quadratic coefficient, variable a, can never have the value of zero (0) because that would result in having a linear equation. The ±, known as the plus-minus sign, means you are required to compute the equation twice: once with using ± as a plus (+) sign and once with using ± as a minus (-) sign. This means that there are actually two different solutions to a quadratic equation.