X^4-256/3x^2-12x

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Solution for X^4-256/3x^2-12x equation:


x in (-oo:+oo)

t_1 = X^4

t_1-256/3*x^2-12*x = 0

t_1-256/3*x^2-12*x = 0

DELTA = (-12)^2-(-256/3*4*t_1)

DELTA = 1024/3*t_1+144

1024/3*t_1+144 = 0

1024/3*t_1+144 = 0 // - 144

1024/3*t_1 = -144 // : 1024/3

t_1 = -144/1024/3

t_1 = -27/64

DELTA = 0 <=> t_2 = -27/64

x = 12/(-256/3*2) i t_1 = -27/64

x = -9/128 i t_1 = -27/64

( x = ((1024/3*t_1+144)^(1/2)+12)/(-256/3*2) or x = (12-(1024/3*t_1+144)^(1/2))/(-256/3*2) ) i t_1 > -27/64

( x = -3/512*((1024/3*t_1+144)^(1/2)+12) or x = -3/512*(12-(1024/3*t_1+144)^(1/2)) ) i t_1 > -27/64

t_1+27/64 > 0

t_1+27/64 > 0 // - 27/64

t_1 > -27/64

x in { -9/128, -3/512*((1024/3*X^4+144)^(1/2)+12), -3/512*(12-(1024/3*X^4+144)^(1/2)) }

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