2x^(2/3)-19x^(1/3)-14=0

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Solution for 2x^(2/3)-19x^(1/3)-14=0 equation: 


x in (-oo:+oo)

2*x^(2/3)-(19*x^(1/3))-14 = 0

2*x^(2/3)-19*x^(1/3)-14 = 0

t_1 = x^(1/3)

2*t_1^2-19*t_1^1-14 = 0

2*t_1^2-19*t_1-14 = 0

DELTA = (-19)^2-(-14*2*4)

DELTA = 473

DELTA > 0

t_1 = (473^(1/2)+19)/(2*2) or t_1 = (19-473^(1/2))/(2*2)

t_1 = (473^(1/2)+19)/4 or t_1 = (19-473^(1/2))/4

t_1 = (19-473^(1/2))/4

x^(1/3)-((19-473^(1/2))/4) = 0

1*x^(1/3) = (19-473^(1/2))/4 // : 1

x^(1/3) = (19-473^(1/2))/4

( (19-473^(1/2))/4 < 0 i 1/3 in (0:1) ) => x należy do O

t_1 = (473^(1/2)+19)/4

x^(1/3)-((473^(1/2)+19)/4) = 0

1*x^(1/3) = (473^(1/2)+19)/4 // : 1

x^(1/3) = (473^(1/2)+19)/4

x^(1/3) = (473^(1/2)+19)/4 // ^ 3

x = ((473^(1/2)+19)^3)/64

x = ((473^(1/2)+19)^3)/64

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