(3/2x)=(4/(2x+75))

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Solution for (3/2x)=(4/(2x+75)) equation: 


D( x )

2*x+75 = 0

2*x+75 = 0

2*x+75 = 0

2*x+75 = 0 // - 75

2*x = -75 // : 2

x = -75/2

x in (-oo:-75/2) U (-75/2:+oo)

(3/2)*x = 4/(2*x+75) // - 4/(2*x+75)

(3/2)*x-(4/(2*x+75)) = 0

(3/2)*x-4*(2*x+75)^-1 = 0

(3*x)/2-4/(2*x+75) = 0

(-4*2)/(2*(2*x+75))+(3*x*(2*x+75))/(2*(2*x+75)) = 0

3*x*(2*x+75)-4*2 = 0

6*x^2+225*x-8 = 0

6*x^2+225*x-8 = 0

6*x^2+225*x-8 = 0

DELTA = 225^2-(-8*4*6)

DELTA = 50817

DELTA > 0

x = (50817^(1/2)-225)/(2*6) or x = (-50817^(1/2)-225)/(2*6)

x = (50817^(1/2)-225)/12 or x = (-(50817^(1/2)+225))/12

(x+(50817^(1/2)+225)/12)*(x-((50817^(1/2)-225)/12)) = 0

((x+(50817^(1/2)+225)/12)*(x-((50817^(1/2)-225)/12)))/(2*(2*x+75)) = 0

((x+(50817^(1/2)+225)/12)*(x-((50817^(1/2)-225)/12)))/(2*(2*x+75)) = 0 // * 2*(2*x+75)

(x+(50817^(1/2)+225)/12)*(x-((50817^(1/2)-225)/12)) = 0

( x+(50817^(1/2)+225)/12 )

x+(50817^(1/2)+225)/12 = 0 // - (50817^(1/2)+225)/12

x = -((50817^(1/2)+225)/12)

( x-((50817^(1/2)-225)/12) )

x-((50817^(1/2)-225)/12) = 0 // + (50817^(1/2)-225)/12

x = (50817^(1/2)-225)/12

x in { -((50817^(1/2)+225)/12), (50817^(1/2)-225)/12 }

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