3x-4=x^(1/2)

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Solution for 3x-4=x^(1/2) equation: 


D( x )

x < 0

x < 0

x in <0:+oo)

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

3*x-x^(1/2)-4 = 0

t_1 = x^(1/2)

3*t_1^2-1*t_1^1-4 = 0

3*t_1^2-t_1-4 = 0

DELTA = (-1)^2-(-4*3*4)

DELTA = 49

DELTA > 0

t_1 = (49^(1/2)+1)/(2*3) or t_1 = (1-49^(1/2))/(2*3)

t_1 = 4/3 or t_1 = -1

t_1 = -1

x^(1/2)+1 = 0

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

x^(1/2) = -1

( -1 < 0 i 1/2 in (0:1) ) => x naleu017Cy do O

t_1 = 4/3

x^(1/2)-4/3 = 0

1*x^(1/2) = 4/3 // : 1

x^(1/2) = 4/3

x^(1/2) = 4/3 // ^ 2

x = 16/9

x = 16/9

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