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Quadratic Formula Calculator

Enter variable coefficients of a second-degree equation and this tool will solve the solution with step-by-step calculations shown.

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This quadratic formula calculator is a tool that helps to solve a quadratic equation by using a quadratic formula or complete the square method. You just have to form of an equation, computation method, and type the parameters of the equation; this quadratic formula solver will work best for you!

What Is The Quadratic Formula?

The quadratic formula is said to be one of the most potent tools in mathematics. This formula is the solution of a second-degree polynomial equation. The standard form of a quadratic equation is mentioned-below:

ax1 + bx + c = 0


  • ‘a’ is the quadratic coefficient
  • ‘x’ is the unknown
  • ‘b’ is the linear coefficient
  • ‘c’ is the constant

The solution of this equation is said to be as the root of the equation. Also, give a try to this simple, but best discriminant calculator online to find the discriminant for the given coefficients for the quadratic, cubic, and quartic equation. Well, a quadratic equation has at most two roots, so solving quadratic equations ultimately means finding the roots of a quadratic equation. However, at first, complex equations are get simplified to make it in standard form. Thus, the values of 'a', 'b', and 'c' are used in the quadratic formula equation to find the roots. The given quadratic formula for finding the roots is:

\[ x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a } \]

In order to analyze the nature of the solution; the discriminant is figured out as: D = b2 – 4ac The b2 – 4ac is said to be as Discriminant.

These two roots are calculated once by putting the positive sign and another one by putting a negative sign.

\[ x₁ = \dfrac{ -b + \sqrt{b^2 - 4ac}}{ 2a } \]

\[ x₂ = \dfrac{ -b - \sqrt{b^2 - 4ac}}{ 2a } \]

Our quadratic formula calculator also uses the same formula to solve quadratic equation. There are three possibilities of getting the roots of quadratic equation, but remember that these possibilities depend upon the value of Discriminant.

  • If b2 – 4ac = 0, then there will be only one root
  • If b2 – 4ac > 0, then there will only two real roots
  • If b2 – 4ac < 0, then there will be two complex roots

Coefficients of a quadratic equation: Also, it is important to note that the numerals i.e. a, b, and c are said to be the coefficient of the equation and they cannot be ‘0’. They all are real numbers that not dependent on x.

If A = 0, then the equation is not said to quadratic, but linear. If B² < 4AC, then the determinant Δ will be negative, it is said to be as this an equation has no real roots. Our quadratic calculator can also help you if you can put the equation in this form:

ax2 + bx + c = 0

How To Use Quadratic Formula Calculator?

Don’t fret; this quadratic equation solver is quite easy to use and loaded with smart and user-friendly interface!


Equation Form:

You have to select the form of equation; this is the form according to which you have to enter the values into the designated fields of our quadratic function calculator. This calculator uses the following form:

  • Ax2 + Bx + C=0 (Standard Form)
  • A(x - H)2 + K =0 (Vertex Form)
  •  A(x-x₁)(x-x₂)= 0 (Factored Form)

Computation Method:

Our quadratic equation calculator allows you to solve the quadratic equation by using the quadratic formula and completing the square method

Enter Values:

If you selected Ax2 + Bx + C=0 form, then you have to enter the values of A, B, and C

If you selected A(x - H)2 + K =0 form, then you have to enter the values of A, H, and K

If you selected A(x-x₁)(x-x₂)= 0 form, then you have to enter the values of A, x1, and x2


Once you entered the above values, then our quadratic equation solver shows the following:

Show The Roots:

This quadratic root calculator shows the root or roots of your given equation.

Show the Simplification:

The calculator simplify the given equation step-by-step.

Show The Discriminant:

If you solve the quadratic equation by using the quadratic formula, then our quadratic discriminant calculator show the discriminant

Show the Quadratic Graph:

This quadratic graph calculator shows you the complete quadratic graph for a given equation!

Frequently Ask Question:

How do you find the quadratic formula?

  • Simply, you just have to complete the square of ax2 + bx + c = 0 to get the quadratic formula
  • You ought to divide both sides of the equation by ‘a’, so the coefficient of x2 is 1
  • So, you ought to rewrite the left side is in the form of x^2+ bx (although in this case, bx is actually

How do you solve quadratic equations?

  • You have to put all the terms on one side of the equal sign, leaving zero on the other side
  • Factor
  • Then, you ought to set each factor equal to zero
  • Very next, you have to solve each of these equations
  • Finally, you have to check by inserting your answer in the original equation

What if there is no B in a quadratic equation?

If the quadratic equation ax2 + bx + c = 0, has no ‘b’ term, then, it means it has the form 〖ax〗^2+ c=0. In such case, you can solve this equation by using the simple square root property.


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