7-1/x-3/x^2=0

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Solution for 7-1/x-3/x^2=0 equation: 


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

7-(1/x)-(3/(x^2)) = 0

7-x^-1-3*x^-2 = 0

t_1 = x^-1

7-3*t_1^2-1*t_1^1 = 0

7-3*t_1^2-t_1 = 0

DELTA = (-1)^2-(-3*4*7)

DELTA = 85

DELTA > 0

t_1 = (85^(1/2)+1)/(-3*2) or t_1 = (1-85^(1/2))/(-3*2)

t_1 = (85^(1/2)+1)/(-6) or t_1 = (1-85^(1/2))/(-6)

t_1 = (85^(1/2)+1)/(-6)

x^-1-((85^(1/2)+1)/(-6)) = 0

1*x^-1 = (85^(1/2)+1)/(-6) // : 1

x^-1 = (85^(1/2)+1)/(-6)

-1 < 0

1/(x^1) = (85^(1/2)+1)/(-6) // * x^1

1 = ((85^(1/2)+1)/(-6))*x^1 // : (85^(1/2)+1)/(-6)

-6*(85^(1/2)+1)^-1 = x^1

x = -6*(85^(1/2)+1)^-1

t_1 = (1-85^(1/2))/(-6)

x^-1-((1-85^(1/2))/(-6)) = 0

1*x^-1 = (1-85^(1/2))/(-6) // : 1

x^-1 = (1-85^(1/2))/(-6)

-1 < 0

1/(x^1) = (1-85^(1/2))/(-6) // * x^1

1 = ((1-85^(1/2))/(-6))*x^1 // : (1-85^(1/2))/(-6)

-6*(1-85^(1/2))^-1 = x^1

x = -6*(1-85^(1/2))^-1

x in { -6*(85^(1/2)+1)^-1, -6*(1-85^(1/2))^-1 }

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