(1/x)+(1/2(x-6))

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Solution for (1/x)+(1/2(x-6)) equation: 


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

(1/2)*(x-6)+1/x = 0

1/2*(x-6)+1/x = 0

(1/2*x*(x-6))/x+1/x = 0

1/2*x*(x-6)+1 = 0

1/2*x^2-3*x+1 = 0

1/2*x^2-3*x+1 = 0

1/2*x^2-3*x+1 = 0

DELTA = (-3)^2-(1/2*1*4)

DELTA = 7

DELTA > 0

x = (7^(1/2)+3)/(1/2*2) or x = (3-7^(1/2))/(1/2*2)

x = 7^(1/2)+3 or x = 3-7^(1/2)

(x+7^(1/2)-3)*(x-7^(1/2)-3) = 0

((x+7^(1/2)-3)*(x-7^(1/2)-3))/x = 0

((x+7^(1/2)-3)*(x-7^(1/2)-3))/x = 0 // * x

(x+7^(1/2)-3)*(x-7^(1/2)-3) = 0

( x+7^(1/2)-3 )

x+7^(1/2)-3 = 0 // - 7^(1/2)-3

x = -(7^(1/2)-3)

x = 3-7^(1/2)

( x-7^(1/2)-3 )

x-7^(1/2)-3 = 0 // + 7^(1/2)+3

x = 7^(1/2)+3

x in { 3-7^(1/2), 7^(1/2)+3 }

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