X^2-8x+16/3x^2-6x-24/2x+5

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Solution for X^2-8x+16/3x^2-6x-24/2x+5 equation: 


x in (-oo:+oo)

t_1 = X^2+5

t_1+16/3*x^2-8*x-6*x-12*x = 0

t_1+16/3*x^2-26*x = 0

DELTA = (-26)^2-(4*16/3*t_1)

DELTA = 676-64/3*t_1

676-64/3*t_1 = 0

676-64/3*t_1 = 0 // - 676

-64/3*t_1 = -676 // : -64/3

t_1 = -676/(-64/3)

t_1 = 507/16

DELTA = 0  <=>  t_2 = 507/16

x = 26/(2*16/3) i t_1 = 507/16

x = 39/16 i t_1 = 507/16

( x = ((676-64/3*t_1)^(1/2)+26)/(2*16/3) or x = (26-(676-64/3*t_1)^(1/2))/(2*16/3) ) i t_1 > 507/16

( x = 3/32*((676-64/3*t_1)^(1/2)+26) or x = 3/32*(26-(676-64/3*t_1)^(1/2)) ) i t_1 > 507/16

t_1-507/16 > 0

t_1-507/16 > 0 // + 507/16

t_1 > 507/16

x in { 39/16, 3/32*((676-64/3*(X^2+5))^(1/2)+26), 3/32*(26-(676-64/3*(X^2+5))^(1/2)) }

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