4/x^2-36/x=19

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Solution for 4/x^2-36/x=19 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)

4/(x^2)-(36/x) = 19 // - 19

4/(x^2)-(36/x)-19 = 0

4/(x^2)-36*x^-1-19 = 0

4*x^-2-36*x^-1-19 = 0

t_1 = x^-1

4*t_1^2-36*t_1^1-19 = 0

4*t_1^2-36*t_1-19 = 0

DELTA = (-36)^2-(-19*4*4)

DELTA = 1600

DELTA > 0

t_1 = (1600^(1/2)+36)/(2*4) or t_1 = (36-1600^(1/2))/(2*4)

t_1 = 19/2 or t_1 = -1/2

t_1 = -1/2

x^-1+1/2 = 0

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

x^-1 = -1/2

-1 < 0

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

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

-2 = x^1

x = -2

t_1 = 19/2

x^-1-19/2 = 0

1*x^-1 = 19/2 // : 1

x^-1 = 19/2

-1 < 0

1/(x^1) = 19/2 // * x^1

1 = 19/2*x^1 // : 19/2

2/19 = x^1

x = 2/19

x in { -2, 2/19 }

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