8x=3(x)^(1/2)

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Solution for 8x=3(x)^(1/2) equation: 


D( x )

x < 0

x < 0

x in <0:+oo)

8*x = 3*x^(1/2) // - 3*x^(1/2)

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

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

t_1 = x^(1/2)

8*t_1^2-3*t_1^1 = 0

8*t_1^2-3*t_1 = 0

DELTA = (-3)^2-(0*4*8)

DELTA = 9

DELTA > 0

t_1 = (9^(1/2)+3)/(2*8) or t_1 = (3-9^(1/2))/(2*8)

t_1 = 3/8 or t_1 = 0

t_1 = 0

x^(1/2)+0 = 0

x^(1/2) = 0

1*x^(1/2) = 0 // : 1

x^(1/2) = 0

x = 0

t_1 = 3/8

x^(1/2)-3/8 = 0

1*x^(1/2) = 3/8 // : 1

x^(1/2) = 3/8

x^(1/2) = 3/8 // ^ 2

x = 9/64

x in { 0, 9/64 }

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