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

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Solution for (3/2x^(1/2))-3x=0 equation: 


D( x )

x < 0

x < 0

x in <0:+oo)

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

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

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

t_1 = x^(1/2)

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

3/2*t_1-3*t_1^2 = 0

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

DELTA = 9/4

DELTA > 0

t_1 = ((9/4)^(1/2)-3/2)/(-3*2) or t_1 = (-(9/4)^(1/2)-3/2)/(-3*2)

t_1 = 0 or t_1 = 1/2

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 = 1/2

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

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

x^(1/2) = 1/2

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

x = 1/4

x in { 0, 1/4 }

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