Quadratic Equation Calculator

The calculator will solve the quadratic equation step by step either by completing the square or using the quadratic formula. It will find both the real and the imaginary (complex) roots.

Enter a quadratic equation:

For example, x^2+4x+3=0 or x^2+4=5x.

Choose a method:

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Solution

Your input: solve the quadratic equation $$$x^{2} - 14 x + 45 = 0$$$ by using quadratic formula.

The standard quadratic equation has the form $$$ax^2+bx+c=0$$$.

In our case, $$$a=1$$$, $$$b=-14$$$, $$$c=45$$$.

Now, find the discriminant using the formula $$$D=b^2-4ac$$$: $$$D=\left(-14\right)^2-4\cdot 1 \cdot 45=16$$$.

Find the roots of the equation using the formulas $$$x_1=\frac{-b-\sqrt{D}}{2a}$$$ and $$$x_2=\frac{-b+\sqrt{D}}{2a}$$$

$$$x_1=\frac{-\left(-14\right)-\sqrt{16}}{2\cdot 1}=5$$$ and $$$x_2=\frac{-\left(-14\right)+\sqrt{16}}{2\cdot 1}=9$$$

Answer: $$$x_1=5$$$; $$$x_2=9$$$