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x^2-8*x+8=0 equation

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Numerical solution:

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The solution

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 2              
x  - 8*x + 8 = 0
$$\left(x^{2} - 8 x\right) + 8 = 0$$
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
$$a = 1$$
$$b = -8$$
$$c = 8$$
, then
D = b^2 - 4 * a * c = 

(-8)^2 - 4 * (1) * (8) = 32

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

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

or
$$x_{1} = 2 \sqrt{2} + 4$$
$$x_{2} = 4 - 2 \sqrt{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -8$$
$$q = \frac{c}{a}$$
$$q = 8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 8$$
$$x_{1} x_{2} = 8$$
The graph
Rapid solution [src]
             ___
x1 = 4 - 2*\/ 2 
$$x_{1} = 4 - 2 \sqrt{2}$$
             ___
x2 = 4 + 2*\/ 2 
$$x_{2} = 2 \sqrt{2} + 4$$
x2 = 2*sqrt(2) + 4
Sum and product of roots [src]
sum
        ___           ___
4 - 2*\/ 2  + 4 + 2*\/ 2 
$$\left(4 - 2 \sqrt{2}\right) + \left(2 \sqrt{2} + 4\right)$$
=
8
$$8$$
product
/        ___\ /        ___\
\4 - 2*\/ 2 /*\4 + 2*\/ 2 /
$$\left(4 - 2 \sqrt{2}\right) \left(2 \sqrt{2} + 4\right)$$
=
8
$$8$$
8
Numerical answer [src]
x1 = 1.17157287525381
x2 = 6.82842712474619
x2 = 6.82842712474619