5/6x-4/3=x^(1/2)

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Solution for 5/6x-4/3=x^(1/2) equation: 


D( x )

x < 0

x < 0

x in <0:+oo)

(5/6)*x-(4/3) = x^(1/2) // - x^(1/2)

(5/6)*x-x^(1/2)-(4/3) = 0

(5/6)*x-x^(1/2)-4/3 = 0

5/6*x-x^(1/2)-4/3 = 0

t_1 = x^(1/2)

5/6*t_1^2-1*t_1^1-4/3 = 0

5/6*t_1^2-t_1-4/3 = 0

DELTA = (-1)^2-(-4/3*5/6*4)

DELTA = 49/9

DELTA > 0

t_1 = ((49/9)^(1/2)+1)/(5/6*2) or t_1 = (1-(49/9)^(1/2))/(5/6*2)

t_1 = 2 or t_1 = -4/5

t_1 = -4/5

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

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

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

( -4/5 < 0 i 1/2 in (0:1) ) => x należy do O

t_1 = 2

x^(1/2)-2 = 0

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

x^(1/2) = 2

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

x = 4

x = 4

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