(2x^2-8x-18)/(2x-4)^2

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Solution for (2x^2-8x-18)/(2x-4)^2 equation: 


D( x )

(2*x-4)^2 = 0

(2*x-4)^2 = 0

(2*x-4)^2 = 0

2*x-4 = 0 // + 4

2*x = 4 // : 2

x = 4/2

x = 2

x in (-oo:2) U (2:+oo)

(2*x^2-(8*x)-18)/((2*x-4)^2) = 0

(2*x^2-8*x-18)/((2*x-4)^2) = 0

2*x^2-8*x-18 = 0

2*(x^2-4*x-9) = 0

x^2-4*x-9 = 0

DELTA = (-4)^2-(-9*1*4)

DELTA = 52

DELTA > 0

x = (52^(1/2)+4)/(1*2) or x = (4-52^(1/2))/(1*2)

x = (2*13^(1/2)+4)/2 or x = (4-2*13^(1/2))/2

2*(x-((4-2*13^(1/2))/2))*(x-((2*13^(1/2)+4)/2)) = 0

(2*(x-((4-2*13^(1/2))/2))*(x-((2*13^(1/2)+4)/2)))/((2*x-4)^2) = 0

( 2 )

2 = 0

x belongs to the empty set

( x-((2*13^(1/2)+4)/2) )

x-((2*13^(1/2)+4)/2) = 0 // + (2*13^(1/2)+4)/2

x = (2*13^(1/2)+4)/2

( x-((4-2*13^(1/2))/2) )

x-((4-2*13^(1/2))/2) = 0 // + (4-2*13^(1/2))/2

x = (4-2*13^(1/2))/2

x in { (2*13^(1/2)+4)/2, (4-2*13^(1/2))/2 }

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