(2x^2-6x-4)/(x-5)

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Solution for (2x^2-6x-4)/(x-5) equation: 


D( x )

x-5 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

x in (-oo:5) U (5:+oo)

(2*x^2-(6*x)-4)/(x-5) = 0

(2*x^2-6*x-4)/(x-5) = 0

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

2*(x^2-3*x-2) = 0

x^2-3*x-2 = 0

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

DELTA = 17

DELTA > 0

x = (17^(1/2)+3)/(1*2) or x = (3-17^(1/2))/(1*2)

x = (17^(1/2)+3)/2 or x = (3-17^(1/2))/2

2*(x-((3-17^(1/2))/2))*(x-((17^(1/2)+3)/2)) = 0

(2*(x-((3-17^(1/2))/2))*(x-((17^(1/2)+3)/2)))/(x-5) = 0

( 2 )

2 = 0

x belongs to the empty set

( x-((17^(1/2)+3)/2) )

x-((17^(1/2)+3)/2) = 0 // + (17^(1/2)+3)/2

x = (17^(1/2)+3)/2

( x-((3-17^(1/2))/2) )

x-((3-17^(1/2))/2) = 0 // + (3-17^(1/2))/2

x = (3-17^(1/2))/2

x in { (17^(1/2)+3)/2, (3-17^(1/2))/2 }

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