x-1/(6-5x)(-4x-1)(-x-7)0

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Solution for x-1/(6-5x)(-4x-1)(-x-7)0 equation: 


D( x )

6-(5*x) = 0

6-(5*x) = 0

6-(5*x) = 0

6-5*x = 0

6-5*x = 0 // - 6

-5*x = -6 // : -5

x = -6/(-5)

x = 6/5

x in (-oo:6/5) U (6/5:+oo)

x-((1/(6-(5*x)))*(-4*x-1)*(-x-7)) < 0

x-((-x-7)*(6-5*x)^-1*(-4*x-1)) < 0

(-1*(-x-7)*(-4*x-1))/(6-5*x)+x < 0

(-1*(-x-7)*(-4*x-1))/(6-5*x)+(x*(6-5*x))/(6-5*x) < 0

x*(6-5*x)-1*(-x-7)*(-4*x-1) < 0

-9*x^2-23*x-7 < 0

-9*x^2-23*x-7 = 0

-1*(9*x^2+23*x+7) = 0

9*x^2+23*x+7 = 0

DELTA = 23^2-(4*7*9)

DELTA = 277

DELTA > 0

x = (277^(1/2)-23)/(2*9) or x = (-277^(1/2)-23)/(2*9)

x = (277^(1/2)-23)/18 or x = (-(277^(1/2)+23))/18

-1*(x+(277^(1/2)+23)/18)*(x-((277^(1/2)-23)/18)) = 0

(-1*(x+(277^(1/2)+23)/18)*(x-((277^(1/2)-23)/18)))/(6-5*x) < 0

(-1*(x+(277^(1/2)+23)/18)*(x-((277^(1/2)-23)/18)))/(6-5*x) < 0 // * (6-5*x)^2

-1*(x+(277^(1/2)+23)/18)*(x-((277^(1/2)-23)/18))*(6-5*x) < 0

( -1 )

-1 < 0

x należy do R

( 6-5*x )

6-5*x < 0 // - 6

-5*x < -6 // : -5

x > -6/(-5)

x > 6/5

( x+(277^(1/2)+23)/18 )

x+(277^(1/2)+23)/18 < 0 // - (277^(1/2)+23)/18

x < -((277^(1/2)+23)/18)

( x-((277^(1/2)-23)/18) )

x-((277^(1/2)-23)/18) < 0 // + (277^(1/2)-23)/18

x < (277^(1/2)-23)/18

	(-oo:-((277^(1/2)+23)/18))	(-((277^(1/2)+23)/18):(277^(1/2)-23)/18)	((277^(1/2)-23)/18:6/5)	(6/5:+oo)
-1	-	-	-	-
6-5*x	+	+	+	-
x+(277^(1/2)+23)/18	-	+	+	+
x-((277^(1/2)-23)/18)	-	-	+	+


x in (-oo:-((277^(1/2)+23)/18)) U ((277^(1/2)-23)/18:6/5)

(-oo:-((277^(1/2)+23)/18)) U ((277^(1/2)-23)/18:6/5)

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