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Your input: solve the quadratic equation $$$x^{2} - 4 x - 12 = 0$$$ by using quadratic formula.

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

In our case, $$$a=1$$$, $$$b=-4$$$, $$$c=-12$$$.

Now, find the discriminant using the formula $$$D=b^2-4ac$$$: $$$D=\left(-4\right)^2-4\cdot 1 \cdot \left(-12\right)=64$$$.

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

$$$x_1=\frac{-\left(-4\right)-\sqrt{64}}{2\cdot 1}=-2$$$ and $$$x_2=\frac{-\left(-4\right)+\sqrt{64}}{2\cdot 1}=6$$$

Answer: $$$x_1=-2$$$; $$$x_2=6$$$