Ln((2x+5)(5x-2)/(x+1))

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Solution for Ln((2x+5)(5x-2)/(x+1)) equation: 


D( x )

((2*x+5)*(5*x-2))/(x+1) <= 0

x+1 = 0

((2*x+5)*(5*x-2))/(x+1) <= 0

((2*x+5)*(5*x-2))/(x+1) <= 0

( 2*x+5 )

2*x+5 <= 0 // - 5

2*x <= -5 // : 2

x <= -5/2

( 5*x-2 )

5*x-2 <= 0 // + 2

5*x <= 2 // : 5

x <= 2/5

( x+1 )

x+1 <= 0 // - 1

x <= -1

(-oo:-5/2)(-5/2:-1)(-1:2/5)(2/5:+oo)2*x+5-+++5*x-2---+x+1--++

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x in (-5/2:-1) U (2/5:+oo)

ln(((2*x+5)*(5*x-2))/(x+1)) = 0

ln(((2*x+5)*(5*x-2))/(x+1)) = ln(e^0)

((2*x+5)*(5*x-2))/(x+1) = e^0

((2*x+5)*(5*x-2))/(x+1)-e^0 = 0

((2*x+5)*(5*x-2))/(x+1)-1 = 0

((2*x+5)*(5*x-2))/(x+1)+(-1*(x+1))/(x+1) = 0

(2*x+5)*(5*x-2)-1*(x+1) = 0

10*x^2+20*x-11 = 0

10*x^2+20*x-11 = 0

10*x^2+20*x-11 = 0

DELTA = 20^2-(-11*4*10)

DELTA = 840

DELTA > 0

x = (840^(1/2)-20)/(2*10) or x = (-840^(1/2)-20)/(2*10)

x = (2*210^(1/2)-20)/20 or x = (-2*210^(1/2)-20)/20

(x-((-2*210^(1/2)-20)/20))*(x-((2*210^(1/2)-20)/20)) = 0

((x-((-2*210^(1/2)-20)/20))*(x-((2*210^(1/2)-20)/20)))/(x+1) = 0

((x-((-2*210^(1/2)-20)/20))*(x-((2*210^(1/2)-20)/20)))/(x+1) = 0 // * x+1

(x-((-2*210^(1/2)-20)/20))*(x-((2*210^(1/2)-20)/20)) = 0

( x-((-2*210^(1/2)-20)/20) )

x-((-2*210^(1/2)-20)/20) = 0 // + (-2*210^(1/2)-20)/20

x = (-2*210^(1/2)-20)/20

( x-((2*210^(1/2)-20)/20) )

x-((2*210^(1/2)-20)/20) = 0 // + (2*210^(1/2)-20)/20

x = (2*210^(1/2)-20)/20

x in { (-2*210^(1/2)-20)/20, (2*210^(1/2)-20)/20 }

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