X^3/6-10x=2x^2/3

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Solution for X^3/6-10x=2x^2/3 equation:


x in (-oo:+oo)

(X^3)/6-(10*x) = (2*x^2)/3 // - (2*x^2)/3

(X^3)/6-((2*x^2)/3)-(10*x) = 0

(X^3)/6+(-2/3)*x^2-10*x = 0

1/6*X^3-2/3*x^2-10*x = 0

DELTA = (-10)^2-(-2/3*1/6*4*X^3)

DELTA = 4/9*X^3+100

4/9*X^3+100 = 0

4/9*X^3 = -100 // : 4/9

X^3 = -225

X^3 = -225 // ^ 1/3

X = -225^(1/3)

DELTA = 0 <=> t_1 = -225^(1/3)

x = 10/(-2/3*2) i X = -225^(1/3)

x = -15/2 i X = -225^(1/3)

( x = ((4/9*X^3+100)^(1/2)+10)/(-2/3*2) or x = (10-(4/9*X^3+100)^(1/2))/(-2/3*2) ) i X > -225^(1/3)

( x = -3/4*((4/9*X^3+100)^(1/2)+10) or x = -3/4*(10-(4/9*X^3+100)^(1/2)) ) i X > -225^(1/3)

X+225^(1/3) > 0

X+225^(1/3) > 0 // - 225^(1/3)

X > -225^(1/3)

x in { -15/2, -3/4*((4/9*X^3+100)^(1/2)+10), -3/4*(10-(4/9*X^3+100)^(1/2)) }

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