(2x-1)(x-4)/x-3

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Solution for (2x-1)(x-4)/x-3 equation: 


D( x )

x = 0

x = 0

x = 0

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

((2*x-1)*(x-4))/x-3 = 0

((2*x-1)*(x-4))/x+(-3*x)/x = 0

(2*x-1)*(x-4)-3*x = 0

2*x^2-12*x+4 = 0

2*x^2-12*x+4 = 0

2*(x^2-6*x+2) = 0

x^2-6*x+2 = 0

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

DELTA = 28

DELTA > 0

x = (28^(1/2)+6)/(1*2) or x = (6-28^(1/2))/(1*2)

x = (2*7^(1/2)+6)/2 or x = (6-2*7^(1/2))/2

2*(x-((6-2*7^(1/2))/2))*(x-((2*7^(1/2)+6)/2)) = 0

(2*(x-((6-2*7^(1/2))/2))*(x-((2*7^(1/2)+6)/2)))/x = 0

(2*(x-((6-2*7^(1/2))/2))*(x-((2*7^(1/2)+6)/2)))/x = 0 // * x

2*(x-((6-2*7^(1/2))/2))*(x-((2*7^(1/2)+6)/2)) = 0

( 2 )

2 = 0

x belongs to the empty set

( x-((2*7^(1/2)+6)/2) )

x-((2*7^(1/2)+6)/2) = 0 // + (2*7^(1/2)+6)/2

x = (2*7^(1/2)+6)/2

( x-((6-2*7^(1/2))/2) )

x-((6-2*7^(1/2))/2) = 0 // + (6-2*7^(1/2))/2

x = (6-2*7^(1/2))/2

x in { (2*7^(1/2)+6)/2, (6-2*7^(1/2))/2 }

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