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Quadratic equation

A quadratic equation is an equation with one unknown x of which the greatest power is 2. The quadratic equation is usually given in the form:

0=a*x^2+b*x+c

where a,b and c are constants and x is the constant.

Solving a quadratic equation

Please enter some of the values from a quadratic equation of the form:
0=a*x^2+b*x+c

a: 
b: 
c: 

Examples of diferent forms of quadratic equations

2*x^2=6*x+4

8=3*x+4+x^2

Solving the quadratic equation

Solving a quadratic equation means finding all values of x that satisfy the equation.

It is very easy to solve quadratic equations, as long as they are having the form

0=a*x^2+b*x+c

If that's not the case, you will have to rewrite the equation, so that it has the same form as the equation above.


Rewriting the equation:

The same value can be added on both sides of the equation

The same value can be subtracted on both sides of the equation

You can multiply by the same value on both sides of the equation (except 0)

You can divide by the same value on both sides of the equation (except 0)

Solving the quadratic equation:

In order to solve the quadratic equation, you must calculate the discriminant:

D=b^2-4*a*c

The discriminant tells us, whether there is zero, one or two solutions (roots)

If D > 0 there is two different solutions/roots
If D = 0 there is one solution/root
If D < 0 there are no solutions/roots

You can then calculate the solutions, which are given by:

x=frac{-b±sqrt{D}}{2*a}