a^7/3+x^2/3+a^1/2+x

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Solution for a^7/3+x^2/3+a^1/2+x equation: 


x in (-oo:+oo)

t_2 = 1/3*a^7+1/2*a

t_2+1/3*x^2+x = 0

t_2+1/3*x^2+x = 0

DELTA = 1^2-(1/3*4*t_2)

DELTA = 1-4/3*t_2

1-4/3*t_2 = 0

1-4/3*t_2 = 0 // - 1

-4/3*t_2 = -1 // : -4/3

t_2 = -1/(-4/3)

t_2 = 3/4

DELTA = 0  <=>  t_3 = 3/4

x = -1/(1/3*2) i t_2 = 3/4

x = -3/2 i t_2 = 3/4

( x = ((1-4/3*t_2)^(1/2)-1)/(1/3*2) or x = (-(1-4/3*t_2)^(1/2)-1)/(1/3*2) ) i t_2 > 3/4

( x = 3/2*((1-4/3*t_2)^(1/2)-1) or x = -3/2*((1-4/3*t_2)^(1/2)+1) ) i t_2 > 3/4

t_2-3/4 > 0

t_2-3/4 > 0 // + 3/4

t_2 > 3/4

x in { -3/2, 3/2*((1-4/3*(1/3*a^7+1/2*a))^(1/2)-1), -3/2*((1-4/3*(1/3*a^7+1/2*a))^(1/2)+1) }

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