5x/x-3+4/x+3=90/x^2-9

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Solution for 5x/x-3+4/x+3=90/x^2-9 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+(5*x)/x-3+3 = 90/(x^2)-9 // - 90/(x^2)-9

4/x-(90/(x^2))+(5*x)/x-3+3+9 = 0

4/x-90*x^-2+(5*x)/x-3+3+9 = 0

4*x^-1-90*x^-2+14 = 0

t_1 = x^-1

4*t_1^1-90*t_1^2+14 = 0

4*t_1-90*t_1^2+14 = 0

DELTA = 4^2-(-90*4*14)

DELTA = 5056

DELTA > 0

t_1 = (5056^(1/2)-4)/(-90*2) or t_1 = (-5056^(1/2)-4)/(-90*2)

t_1 = (8*79^(1/2)-4)/(-180) or t_1 = (-8*79^(1/2)-4)/(-180)

t_1 = (8*79^(1/2)-4)/(-180)

x^-1-((8*79^(1/2)-4)/(-180)) = 0

1*x^-1 = (8*79^(1/2)-4)/(-180) // : 1

x^-1 = (8*79^(1/2)-4)/(-180)

-1 < 0

1/(x^1) = (8*79^(1/2)-4)/(-180) // * x^1

1 = ((8*79^(1/2)-4)/(-180))*x^1 // : (8*79^(1/2)-4)/(-180)

-180*(8*79^(1/2)-4)^-1 = x^1

x = -180*(8*79^(1/2)-4)^-1

t_1 = (-8*79^(1/2)-4)/(-180)

x^-1-((-8*79^(1/2)-4)/(-180)) = 0

1*x^-1 = (-8*79^(1/2)-4)/(-180) // : 1

x^-1 = (-8*79^(1/2)-4)/(-180)

-1 < 0

1/(x^1) = (-8*79^(1/2)-4)/(-180) // * x^1

1 = ((-8*79^(1/2)-4)/(-180))*x^1 // : (-8*79^(1/2)-4)/(-180)

-180*(-8*79^(1/2)-4)^-1 = x^1

x = -180*(-8*79^(1/2)-4)^-1

x in { -180*(8*79^(1/2)-4)^-1, -180*(-8*79^(1/2)-4)^-1 }

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