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x^2-6*x+4=0

x^2-6*x+4=0 equation

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Numerical solution:

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The solution

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 2              
x  - 6*x + 4 = 0
(x2−6x)+4=0\left(x^{2} - 6 x\right) + 4 = 0
Simplify
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:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=1a = 1
b=−6b = -6
c=4c = 4
, then
D = b^2 - 4 * a * c = 

(-6)^2 - 4 * (1) * (4) = 20

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

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

or
x1=5+3x_{1} = \sqrt{5} + 3
x2=3−5x_{2} = 3 - \sqrt{5}
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−6p = -6
q=caq = \frac{c}{a}
q=4q = 4
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=6x_{1} + x_{2} = 6
x1x2=4x_{1} x_{2} = 4
The graph
05-10-5101520-200200
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
           ___
x1 = 3 - \/ 5
x1=3−5x_{1} = 3 - \sqrt{5} 
           ___
x2 = 3 + \/ 5
x2=5+3x_{2} = \sqrt{5} + 3 
x2 = sqrt(5) + 3
Sum and product of roots [src] 
sum
      ___         ___
3 - \/ 5  + 3 + \/ 5
(3−5)+(5+3)\left(3 - \sqrt{5}\right) + \left(\sqrt{5} + 3\right) 
=
6
66 
product
/      ___\ /      ___\
\3 - \/ 5 /*\3 + \/ 5 /
(3−5)(5+3)\left(3 - \sqrt{5}\right) \left(\sqrt{5} + 3\right) 
=
4
44 
4
Numerical answer [src] 
x1 = 5.23606797749979
x2 = 0.76393202250021
x2 = 0.76393202250021
The graph
x^2-6*x+4=0 equation
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