7,9*10^-3=(2y/(1-2y))^2

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Solution for 7,9*10^-3=(2y/(1-2y))^2 equation: 


D( y )

1-(2*y) = 0

1-(2*y) = 0

1-(2*y) = 0

1-2*y = 0

1-2*y = 0 // - 1

-2*y = -1 // : -2

y = -1/(-2)

y = 1/2

y in (-oo:1/2) U (1/2:+oo)

7.9*10^-3 = ((2*y)/(1-(2*y)))^2 // - ((2*y)/(1-(2*y)))^2

7.9*10^-3-((2*y)/(1-(2*y)))^2 = 0

7.9*10^-3-((2*y)/(1-2*y))^2 = 0

(-1*(2*y)^2)/((1-2*y)^2)+0.0079 = 0

(-1*(2*y)^2)/((1-2*y)^2)+(0.0079*(1-2*y)^2)/((1-2*y)^2) = 0

0.0079*(1-2*y)^2-1*(2*y)^2 = 0

0.0079-3.9684*y^2-0.0316*y = 0

0.0079-3.9684*y^2-0.0316*y = 0

0.0079-3.9684*y^2-0.0316*y = 0

DELTA = (-0.0316)^2-(-3.9684*0.0079*4)

DELTA = 0.0316^2+0.12540144

DELTA = 0.1264

DELTA > 0

y = ((0.0316^2+0.12540144)^(1/2)+0.0316)/(-3.9684*2) or y = (0.0316-(0.0316^2+0.12540144)^(1/2))/(-3.9684*2)

y = -0.12599536*((0.0316^2+0.12540144)^(1/2)+0.0316) or y = -0.12599536*(0.0316-(0.0316^2+0.12540144)^(1/2))

(y+0.12599536*((0.0316^2+0.12540144)^(1/2)+0.0316))*(y+0.12599536*(0.0316-(0.0316^2+0.12540144)^(1/2))) = 0

((y+0.12599536*((0.0316^2+0.12540144)^(1/2)+0.0316))*(y+0.12599536*(0.0316-(0.0316^2+0.12540144)^(1/2))))/((1-2*y)^2) = 0

((y+0.12599536*((0.0316^2+0.12540144)^(1/2)+0.0316))*(y+0.12599536*(0.0316-(0.0316^2+0.12540144)^(1/2))))/((1-2*y)^2) = 0 // * (1-2*y)^2

(y+0.12599536*((0.0316^2+0.12540144)^(1/2)+0.0316))*(y+0.12599536*(0.0316-(0.0316^2+0.12540144)^(1/2))) = 0

( y+0.12599536*((0.0316^2+0.12540144)^(1/2)+0.0316) )

y+0.12599536*((0.0316^2+0.12540144)^(1/2)+0.0316) = 0 // - 0.12599536*((0.0316^2+0.12540144)^(1/2)+0.0316)

y = -(0.12599536*((0.0316^2+0.12540144)^(1/2)+0.0316))

y = -0.12599536*((0.0316^2+0.12540144)^(1/2)+0.0316)

( y+0.12599536*(0.0316-(0.0316^2+0.12540144)^(1/2)) )

y+0.12599536*(0.0316-(0.0316^2+0.12540144)^(1/2)) = 0 // - 0.12599536*(0.0316-(0.0316^2+0.12540144)^(1/2))

y = -(0.12599536*(0.0316-(0.0316^2+0.12540144)^(1/2)))

y = -0.12599536*(0.0316-(0.0316^2+0.12540144)^(1/2))

y in { -0.12599536*((0.0316^2+0.12540144)^(1/2)+0.0316), -0.12599536*(0.0316-(0.0316^2+0.12540144)^(1/2)) }

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