x^2-x=26-120/x^2-x

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Solution for x^2-x=26-120/x^2-x 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 = 26-x-(120/(x^2)) // - 26-x-(120/(x^2))

x^2-x+x+120/(x^2)-26 = 0

x^2+120*x^-2-26 = 0

t_1 = x^2

1*t_1^1+120*t_1^-1-26 = 0

1*t_1^1+120*t_1^-1-26*t_1^0 = 0

(1*t_1^2-26*t_1^1+120*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^2-26*t_1^1+120*t_1^0) = 0

t_1^1

t_1^2-26*t_1+120 = 0

t_1^2-26*t_1+120 = 0

DELTA = (-26)^2-(1*4*120)

DELTA = 196

DELTA > 0

t_1 = (196^(1/2)+26)/(1*2) or t_1 = (26-196^(1/2))/(1*2)

t_1 = 20 or t_1 = 6

t_1 in { 6, 20} 

t_1 = 6

x^2-6 = 0

1*x^2 = 6 // : 1

x^2 = 6

x^2 = 6 // ^ 1/2

abs(x) = 6^(1/2)

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

t_1 = 20

x^2-20 = 0

1*x^2 = 20 // : 1

x^2 = 20

x^2 = 20 // ^ 1/2

abs(x) = 2*5^(1/2)

x = 2*5^(1/2) or x = -(2*5^(1/2))

x in { 6^(1/2), -6^(1/2), 2*5^(1/2), -(2*5^(1/2)) }

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