(2z^2-12z-8)/(2z)

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Solution for (2z^2-12z-8)/(2z) equation: 


D( z )

2*z = 0

2*z = 0

2*z = 0

2*z = 0 // : 2

z = 0

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

(2*z^2-(12*z)-8)/(2*z) = 0

(2*z^2-12*z-8)/(2*z) = 0

2*z^2-12*z-8 = 0

2*(z^2-6*z-4) = 0

z^2-6*z-4 = 0

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

DELTA = 52

DELTA > 0

z = (52^(1/2)+6)/(1*2) or z = (6-52^(1/2))/(1*2)

z = (2*13^(1/2)+6)/2 or z = (6-2*13^(1/2))/2

2*(z-((6-2*13^(1/2))/2))*(z-((2*13^(1/2)+6)/2)) = 0

(2*(z-((6-2*13^(1/2))/2))*(z-((2*13^(1/2)+6)/2)))/(2*z) = 0

( 2 )

2 = 0

z belongs to the empty set

( z-((2*13^(1/2)+6)/2) )

z-((2*13^(1/2)+6)/2) = 0 // + (2*13^(1/2)+6)/2

z = (2*13^(1/2)+6)/2

( z-((6-2*13^(1/2))/2) )

z-((6-2*13^(1/2))/2) = 0 // + (6-2*13^(1/2))/2

z = (6-2*13^(1/2))/2

z in { (2*13^(1/2)+6)/2, (6-2*13^(1/2))/2 }

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