77/x^2=19/x+6

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Solution for 77/x^2=19/x+6 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)

77/(x^2) = 19/x+6 // - 19/x+6

77/(x^2)-(19/x)-6 = 0

77/(x^2)-19*x^-1-6 = 0

77*x^-2-19*x^-1-6 = 0

t_1 = x^-1

77*t_1^2-19*t_1^1-6 = 0

77*t_1^2-19*t_1-6 = 0

DELTA = (-19)^2-(-6*4*77)

DELTA = 2209

DELTA > 0

t_1 = (2209^(1/2)+19)/(2*77) or t_1 = (19-2209^(1/2))/(2*77)

t_1 = 3/7 or t_1 = -2/11

t_1 = -2/11

x^-1+2/11 = 0

1*x^-1 = -2/11 // : 1

x^-1 = -2/11

-1 < 0

1/(x^1) = -2/11 // * x^1

1 = -2/11*x^1 // : -2/11

-11/2 = x^1

x = -11/2

t_1 = 3/7

x^-1-3/7 = 0

1*x^-1 = 3/7 // : 1

x^-1 = 3/7

-1 < 0

1/(x^1) = 3/7 // * x^1

1 = 3/7*x^1 // : 3/7

7/3 = x^1

x = 7/3

x in { -11/2, 7/3 }

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