(2x-9)^2/3(x-4)^1/3

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Solution for (2x-9)^2/3(x-4)^1/3 equation: 


x in (-oo:+oo)

((2*x-9)^2)/3 > ((x-4)^1)/3 // - ((x-4)^1)/3

((2*x-9)^2)/3-(((x-4)^1)/3) > 0

((2*x-9)^2)/3-((x-4)/3) > 0

((2*x-9)^2)/3+(-1*(x-4))/3 > 0

(2*x-9)^2-1*(x-4) > 0

4*x^2-37*x+85 > 0

4*x^2-37*x+85 = 0

4*x^2-37*x+85 = 0

DELTA = (-37)^2-(4*4*85)

DELTA = 9

DELTA > 0

x = (9^(1/2)+37)/(2*4) or x = (37-9^(1/2))/(2*4)

x = 5 or x = 17/4

(x-17/4)*(x-5) = 0

((x-17/4)*(x-5))/3 > 0

((x-17/4)*(x-5))/3 > 0 // * 3^2

3*(x-17/4)*(x-5) > 0

( 3 )

3 > 0

x należy do R

( x-17/4 )

x-17/4 > 0 // + 17/4

x > 17/4

( x-5 )

x-5 > 0 // + 5

x > 5

	(-oo:17/4)	(17/4:5)	(5:+oo)
3	+	+	+
x-17/4	-	+	+
x-5	-	-	+


x in (-oo:17/4) U (5:+oo)

(-oo:17/4) U (5:+oo)

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