Quadratic Equations Calculator


This calculator allows you to obtain one or both solutions to a quadratic equation. The solutions include imaginary numbers.

How to use the quadratic equation calculator?

Step 1: Enter the quadratic equation in the first input box. The equation can contain any variable. Entering an expression without an equal sign will assume that the expression is 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 input box. If the quadratic equation is 2x^2+x+5=0, you must enter x in the second box.

Step 3: Click "Solve" to get the solution(s) as appropriate.

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

How to enter equations into the calculator?

To enter equations, you can use any variable as long as you indicate the variable used in the second 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 nonzero. 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, factoring and using the quadratic formula.

Solving 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).

Solving quadratic equations using the quadratic formula

Another way to solve any quadratic equation is to use 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 coefficients a=3, b=5, and c=3.

This formula returns a 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 get only one real solution.

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

Related calculators:

You can explore other calculators here.