7x^4-7x^3+x^2/X

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Solution for 7x^4-7x^3+x^2/X equation: 


x in (-oo:+oo)

(x^2)/X+7*x^4-(7*x^3) = 0

(x^2)/X+7*x^4-7*x^3 = 0

X^-1*x^2+7*x^4-7*x^3 = 0

x^2*(X^-1+7*x^2-7*x) = 0

X^-1+7*x^2-7*x = 0

DELTA = (-7)^2-(4*7*X^-1)

DELTA = 49-28*X^-1

49-28*X^-1 = 0

-28*X^-1 = -49 // : -28

X^-1 = 7/4

-1 < 0

1/(X^1) = 7/4 // * X^1

1 = 7/4*X^1 // : 7/4

4/7 = X^1

X = 4/7

DELTA = 0  <=>  t_1 = 4/7

x = 7/(2*7) i X = 4/7

x = 1/2 i X = 4/7

( x = ((49-28*X^-1)^(1/2)+7)/(2*7) or x = (7-(49-28*X^-1)^(1/2))/(2*7) ) i X > 4/7

( x = ((49-28*X^-1)^(1/2)+7)/14 or x = (7-(49-28*X^-1)^(1/2))/14 ) i X > 4/7

X-4/7 > 0

X-4/7 > 0 // + 4/7

X > 4/7

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in { 1/2, ((49-28*X^-1)^(1/2)+7)/14, (7-(49-28*X^-1)^(1/2))/14, 0 }

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