12x^(4/5)=23x^(2/5)-10

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Solution for 12x^(4/5)=23x^(2/5)-10 equation: 


x in (-oo:+oo)

12*x^(4/5) = 23*x^(2/5)-10 // - 23*x^(2/5)-10

12*x^(4/5)-(23*x^(2/5))+10 = 0

12*x^(4/5)-23*x^(2/5)+10 = 0

t_1 = x^(2/5)

12*t_1^2-23*t_1^1+10 = 0

12*t_1^2-23*t_1+10 = 0

DELTA = (-23)^2-(4*10*12)

DELTA = 49

DELTA > 0

t_1 = (49^(1/2)+23)/(2*12) or t_1 = (23-49^(1/2))/(2*12)

t_1 = 5/4 or t_1 = 2/3

t_1 = 2/3

x^(2/5)-2/3 = 0

1*x^(2/5) = 2/3 // : 1

x^(2/5) = 2/3

x^(2/5) = 2/3 // ^ 5

x^2 = 32/243 // ^ 1/2

abs(x) = (32/243)^(1/2)

x = (32/243)^(1/2) or x = -(32/243)^(1/2)

t_1 = 5/4

x^(2/5)-5/4 = 0

1*x^(2/5) = 5/4 // : 1

x^(2/5) = 5/4

x^(2/5) = 5/4 // ^ 5

x^2 = 3125/1024 // ^ 1/2

abs(x) = (3125/1024)^(1/2)

x = (3125/1024)^(1/2) or x = -(3125/1024)^(1/2)

x in { (32/243)^(1/2), -(32/243)^(1/2), (3125/1024)^(1/2), -(3125/1024)^(1/2) }

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