二次方程式計算機

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