4x^(8/5)=10x^(4/5)-4

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Solution for 4x^(8/5)=10x^(4/5)-4 equation: 


x in (-oo:+oo)

4*x^(8/5) = 10*x^(4/5)-4 // - 10*x^(4/5)-4

4*x^(8/5)-(10*x^(4/5))+4 = 0

4*x^(8/5)-10*x^(4/5)+4 = 0

t_1 = x^(4/5)

4*t_1^2-10*t_1^1+4 = 0

4*t_1^2-10*t_1+4 = 0

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

DELTA = 36

DELTA > 0

t_1 = (36^(1/2)+10)/(2*4) or t_1 = (10-36^(1/2))/(2*4)

t_1 = 2 or t_1 = 1/2

t_1 = 1/2

x^(4/5)-1/2 = 0

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

x^(4/5) = 1/2

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

x^4 = 1/32 // ^ 1/4

abs(x) = (1/32)^(1/4)

x = (1/32)^(1/4) or x = -(1/32)^(1/4)

t_1 = 2

x^(4/5)-2 = 0

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

x^(4/5) = 2

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

x^4 = 32 // ^ 1/4

abs(x) = 2*2^(1/4)

x = 2*2^(1/4) or x = -(2*2^(1/4))

x in { (1/32)^(1/4), -(1/32)^(1/4), 2*2^(1/4), -(2*2^(1/4)) }

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