x^2-25/3-x/3x+15/x^2-9

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Solution for x^2-25/3-x/3x+15/x^2-9 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

x^2-((x/3)*x)+15/(x^2)-(25/3)-9 = 0

x^2+(-1/3)*x^2+15/(x^2)-25/3-9 = 0

2/3*x^2+15*x^-2-52/3 = 0

t_1 = x^2

2/3*t_1^1+15*t_1^-1-52/3 = 0

2/3*t_1^1+15*t_1^-1-52/3*t_1^0 = 0

(2/3*t_1^2-52/3*t_1^1+15*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(2/3*t_1^2-52/3*t_1^1+15*t_1^0) = 0

t_1^1

(2/3)*t_1^2+(-52/3)*t_1+15 = 0

(2/3)*t_1^2+(-52/3)*t_1+15 = 0

DELTA = (-52/3)^2-(4*15*(2/3))

DELTA = 2344/9

DELTA > 0

t_1 = ((2344/9)^(1/2)-(-52/3))/(2*(2/3)) or t_1 = (-(-52/3)-(2344/9)^(1/2))/(2*(2/3))

t_1 = 3/4*((2344/9)^(1/2)+52/3) or t_1 = 3/4*(52/3-(2344/9)^(1/2))

t_1 in { 3/4*(52/3-(2344/9)^(1/2)), 3/4*((2344/9)^(1/2)+52/3)} 

t_1 = 3/4*(52/3-(2344/9)^(1/2))

x^2-(3/4*(52/3-(2344/9)^(1/2))) = 0

x^2-3/4*(52/3-(2344/9)^(1/2)) = 0

1*x^2 = -(-3/4*(52/3-(2344/9)^(1/2))) // : 1

x^2 = 3/4*(52/3-(2344/9)^(1/2))

x^2 = 3/4*(52/3-(2344/9)^(1/2)) // ^ 1/2

abs(x) = (3/4)^(1/2)*(52/3-(2344/9)^(1/2))^(1/2)

x = (3/4)^(1/2)*(52/3-(2344/9)^(1/2))^(1/2) or x = -((3/4)^(1/2)*(52/3-(2344/9)^(1/2))^(1/2))

t_1 = 3/4*((2344/9)^(1/2)+52/3)

x^2-(3/4*((2344/9)^(1/2)+52/3)) = 0

x^2-3/4*((2344/9)^(1/2)+52/3) = 0

1*x^2 = -(-3/4*((2344/9)^(1/2)+52/3)) // : 1

x^2 = 3/4*((2344/9)^(1/2)+52/3)

x^2 = 3/4*((2344/9)^(1/2)+52/3) // ^ 1/2

abs(x) = (3/4)^(1/2)*((2344/9)^(1/2)+52/3)^(1/2)

x = (3/4)^(1/2)*((2344/9)^(1/2)+52/3)^(1/2) or x = -((3/4)^(1/2)*((2344/9)^(1/2)+52/3)^(1/2))

x in { (3/4)^(1/2)*(52/3-(2344/9)^(1/2))^(1/2), -((3/4)^(1/2)*(52/3-(2344/9)^(1/2))^(1/2)), (3/4)^(1/2)*((2344/9)^(1/2)+52/3)^(1/2), -((3/4)^(1/2)*((2344/9)^(1/2)+52/3)^(1/2)) }

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