(5y/y-5)-(25/y+5)=250/(y^2)-25

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Solution for (5y/y-5)-(25/y+5)=250/(y^2)-25 equation:


D( y )

y = 0

y^2 = 0

y = 0

y = 0

y^2 = 0

y^2 = 0

1*y^2 = 0 // : 1

y^2 = 0

y = 0

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

(5*y)/y-(25/y)-5-5 = 250/(y^2)-25 // - 250/(y^2)-25

(5*y)/y-(25/y)-(250/(y^2))-5-5+25 = 0

(5*y)/y-25*y^-1-250*y^-2-5-5+25 = 0

20-25*y^-1-250*y^-2 = 0

t_1 = y^-1

20-250*t_1^2-25*t_1^1 = 0

20-250*t_1^2-25*t_1 = 0

DELTA = (-25)^2-(-250*4*20)

DELTA = 20625

DELTA > 0

t_1 = (20625^(1/2)+25)/(-250*2) or t_1 = (25-20625^(1/2))/(-250*2)

t_1 = (25*33^(1/2)+25)/(-500) or t_1 = (25-25*33^(1/2))/(-500)

t_1 = (25*33^(1/2)+25)/(-500)

y^-1-((25*33^(1/2)+25)/(-500)) = 0

1*y^-1 = (25*33^(1/2)+25)/(-500) // : 1

y^-1 = (25*33^(1/2)+25)/(-500)

-1 < 0

1/(y^1) = (25*33^(1/2)+25)/(-500) // * y^1

1 = ((25*33^(1/2)+25)/(-500))*y^1 // : (25*33^(1/2)+25)/(-500)

-500*(25*33^(1/2)+25)^-1 = y^1

y = -500*(25*33^(1/2)+25)^-1

t_1 = (25-25*33^(1/2))/(-500)

y^-1-((25-25*33^(1/2))/(-500)) = 0

1*y^-1 = (25-25*33^(1/2))/(-500) // : 1

y^-1 = (25-25*33^(1/2))/(-500)

-1 < 0

1/(y^1) = (25-25*33^(1/2))/(-500) // * y^1

1 = ((25-25*33^(1/2))/(-500))*y^1 // : (25-25*33^(1/2))/(-500)

-500*(25-25*33^(1/2))^-1 = y^1

y = -500*(25-25*33^(1/2))^-1

y in { -500*(25*33^(1/2)+25)^-1, -500*(25-25*33^(1/2))^-1 }

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