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x^2-6*x-3=0

x^2-6*x-3=0 equation

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Numerical solution:

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The solution

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 2              
x  - 6*x - 3 = 0
$$\left(x^{2} - 6 x\right) - 3 = 0$$
Detail solution
This equation is of the form
a*x^2 + b*x + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -6$$
$$c = -3$$
, then
D = b^2 - 4 * a * c = 

(-6)^2 - 4 * (1) * (-3) = 48

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
$$x_{1} = 3 + 2 \sqrt{3}$$
$$x_{2} = 3 - 2 \sqrt{3}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = -3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 6$$
$$x_{1} x_{2} = -3$$
The graph
Sum and product of roots [src]
sum
        ___           ___
3 - 2*\/ 3  + 3 + 2*\/ 3 
$$\left(3 - 2 \sqrt{3}\right) + \left(3 + 2 \sqrt{3}\right)$$
=
6
$$6$$
product
/        ___\ /        ___\
\3 - 2*\/ 3 /*\3 + 2*\/ 3 /
$$\left(3 - 2 \sqrt{3}\right) \left(3 + 2 \sqrt{3}\right)$$
=
-3
$$-3$$
-3
Rapid solution [src]
             ___
x1 = 3 - 2*\/ 3 
$$x_{1} = 3 - 2 \sqrt{3}$$
             ___
x2 = 3 + 2*\/ 3 
$$x_{2} = 3 + 2 \sqrt{3}$$
x2 = 3 + 2*sqrt(3)
Numerical answer [src]
x1 = -0.464101615137755
x2 = 6.46410161513775
x2 = 6.46410161513775
The graph
x^2-6*x-3=0 equation