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x^2-6x+7=0

x^2-6x+7=0 equation

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Numerical solution:

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The solution

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 2              
x  - 6*x + 7 = 0
$$\left(x^{2} - 6 x\right) + 7 = 0$$
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
$$a = 1$$
$$b = -6$$
$$c = 7$$
, then
D = b^2 - 4 * a * c = 

(-6)^2 - 4 * (1) * (7) = 8

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

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

or
$$x_{1} = \sqrt{2} + 3$$
$$x_{2} = 3 - \sqrt{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = 7$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 6$$
$$x_{1} x_{2} = 7$$
The graph
Rapid solution [src]
           ___
x1 = 3 - \/ 2 
$$x_{1} = 3 - \sqrt{2}$$
           ___
x2 = 3 + \/ 2 
$$x_{2} = \sqrt{2} + 3$$
x2 = sqrt(2) + 3
Sum and product of roots [src]
sum
      ___         ___
3 - \/ 2  + 3 + \/ 2 
$$\left(3 - \sqrt{2}\right) + \left(\sqrt{2} + 3\right)$$
=
6
$$6$$
product
/      ___\ /      ___\
\3 - \/ 2 /*\3 + \/ 2 /
$$\left(3 - \sqrt{2}\right) \left(\sqrt{2} + 3\right)$$
=
7
$$7$$
7
Numerical answer [src]
x1 = 4.41421356237309
x2 = 1.5857864376269
x2 = 1.5857864376269
The graph
x^2-6x+7=0 equation