Quadratic Equations Calculator

Enter the quadratic equation and the variable to solve for. For example, enter 2x^2+3x-2=0 and x to solve the equation for x.



Solutions:

Examples:

  • To solve \(2x^2+3x-2=0\), enter 2x^2+3x-2=0 and the variable x.
  • To solve \(\frac{2}{3}t^2+\frac{4}{3}t=0\), enter 2/3t^2+4/3t=0 and the variable t.

This calculator allows you to obtain one solution or both solutions to a quadratic equation. The solutions will include imaginary numbers if real number solutions are not possible.

How to use quadratic equations calculator?

Step 1: Enter the quadratic equation in the first input box. The equation can contain any variable. When entering an expression without the equals sign, the expression will be assumed to be equal to 0. For example, 2x^2+x+5 will be interpreted as 2x^2+x+5=0.

Step 2: Enter the variable to solve for in the second iput box. If the quadratic equation is 2x^2+x+5=0, you must enter x in the second input box.

Step 3: Click “Solve” to get the solution(s).

Step 4: The solution(s) will be displayed at the bottom of the calculator.

How to enter equations in the calculator?

To enter equations, you can use any variable as long as you indicate the variable used in the second input box. Use the ^ sign to indicate an exponent. For example, to enter the equation \(3x^2+2x+5=0\), enter 3x^2+2x+5=0.

You can also enter fractional coefficients. For example, to enter the equation \(\frac{1}{2}x^2+\frac{2}{3}x+5=0\), enter 1/2x^2+2/3x+5.

What are quadratic equations?

Quadratic equations or second-degree equations are equations of the form \(x^2+bx+c=0\), where a is different from zero. These equations have variables with a power of 2.

Quadratic equations can have one solution, two solutions, or no solution (if we only consider real numbers).

How to find solutions to quadratic equations?

We can use two main methods to find solutions to quadratic equations, by factoring and by using the quadratic formula.

Solve quadratic equations by factoring

It is possible to find solutions to quadratic equations by factoring the equation. For example, we can factor \( x^2+3x+2=0\) to form \((x+2)(x+1)=0\). In the factored form, we can easily find the solutions, which are \( x=-2, ~x=-1\).

Solve quadratic equations by using the quadratic formula

Another way to solve any quadratic equation is by using the quadratic formula:

\(x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)

where, a, b and c are the coefficients of the equation.

For example, in the equation \(3x^2+5x+3=0\), we have the coefficients a=3, b=5, and c=3.

This formula returns one solution or both solutions to the quadratic equation if applicable. The expression inside the square root determines the nature of the solutions. If the expression is equal to 0, we will obtain a single real solution.

On the other hand, if the expression inside the square root is positive, we will obtain two real solutions. Finally, if the expression is negative, we will obtain two imaginary solutions.

Related calculators

You can explore other calculators here.