18x^4-24X^3+15x/3x

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Solution for 18x^4-24X^3+15x/3x equation: 


x in (-oo:+oo)

18*x^4-(24*X^3)+((15*x)/3)*x = 0

18*x^4-24*X^3+((15*x)/3)*x = 0

18*x^4-24*X^3+5*x^2 = 0

t_1 = x^2

18*t_1^2-24*X^3+5*t_1^1 = 0

18*t_1^2-24*X^3+5*t_1 = 0

DELTA = 5^2-(-24*4*18*X^3)

DELTA = 1728*X^3+25

1728*X^3+25 = 0

1728*X^3 = -25 // : 1728

X^3 = -25/1728

X^3 = -25/1728 // ^ 1/3

X = -(25/1728)^(1/3)

DELTA = 0  <=>  t_2 = -(25/1728)^(1/3)

t_1 = -5/(2*18) i X = -(25/1728)^(1/3)

t_1 = -5/36 i X = -(25/1728)^(1/3)

( t_1 = ((1728*X^3+25)^(1/2)-5)/(2*18) or t_1 = (-(1728*X^3+25)^(1/2)-5)/(2*18) ) i X > -(25/1728)^(1/3)

( t_1 = ((1728*X^3+25)^(1/2)-5)/36 or t_1 = (-((1728*X^3+25)^(1/2)+5))/36 ) i X > -(25/1728)^(1/3)

X+(25/1728)^(1/3) > 0

X+(25/1728)^(1/3) > 0 // - (25/1728)^(1/3)

X > -(25/1728)^(1/3)

t_1 = -5/36

x^2+5/36 = 0

1*x^2 = -5/36 // : 1

x^2 = -5/36

t_1 = ((1728*X^3+25)^(1/2)-5)/36

t_3 = -(((1728*X^3+25)^(1/2)-5)/36)

t_3+x^2 = 0

1*x^2 = -t_3 // : 1

x^2 = -t_3

x^2 = -t_3 // ^ 1/2

abs(x) = (-t_3)^(1/2)

x = (-t_3)^(1/2) or x = -(-t_3)^(1/2)

t_1 = (-((1728*X^3+25)^(1/2)+5))/36

t_4 = (1/36)*((1728*X^3+25)^(1/2)+5)

t_4+x^2 = 0

1*x^2 = -t_4 // : 1

x^2 = -t_4

x^2 = -t_4 // ^ 1/2

abs(x) = (-t_4)^(1/2)

x = (-t_4)^(1/2) or x = -(-t_4)^(1/2)

x in { (((1728*X^3+25)^(1/2)-5)/36)^(1/2), -(((1728*X^3+25)^(1/2)-5)/36)^(1/2), (-((1/36)*((1728*X^3+25)^(1/2)+5)))^(1/2), -(-((1/36)*((1728*X^3+25)^(1/2)+5)))^(1/2) }

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