Online quadratic equation solver

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The calculator

The calculator below makes use of the quadratic formula to solve the quadratic equation:

Simply enter the values for the coefficients a, b, c, and click “Calculate solution” to find the solution to the equation.

Where does the quadratic formula come from?

There is no magic, but only logical reasoning. We can safely assume that the coefficient a is nonzero (otherwise, it wouldn't be a quadratic equation). This allows us to factorize the polynomial by a. Since a is nonzero, the remaining factor must be zero:

What makes the solution to the above equation not obvious is that the variable x appears in two different places, in the quadratic term (x²) and in the linear term (bx/a). In order to solve this problem, the idea is to notice that:

While x appears in two different places in the left-hand side, it appears only in one place in the right-hand side. Therefore, the equation can be rewritten as:

The equation is now easy to solve. First, we move the last term to the right side:

Then we take the squareroot on both sides of the equation by keeping in mind that two squares are equal if either their squareroots are equal or opposite. This gives two solutions:

Finally, we isolate x:

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