5x/(2x+1)+8/(4x+2)=8/3

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Solution for 5x/(2x+1)+8/(4x+2)=8/3 equation: 


D( x )

2*x+1 = 0

4*x+2 = 0

2*x+1 = 0

2*x+1 = 0

2*x+1 = 0 // - 1

2*x = -1 // : 2

x = -1/2

4*x+2 = 0

4*x+2 = 0

4*x+2 = 0 // - 2

4*x = -2 // : 4

x = -2/4

x = -1/2

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

(5*x)/(2*x+1)+8/(4*x+2) = 8/3 // - 8/3

(5*x)/(2*x+1)+8/(4*x+2)-(8/3) = 0

(5*x)/(2*x+1)+8/(4*x+2)-8/3 = 0

(3*5*x*(4*x+2))/(3*(2*x+1)*(4*x+2))+(3*8*(2*x+1))/(3*(2*x+1)*(4*x+2))+(-8*(2*x+1)*(4*x+2))/(3*(2*x+1)*(4*x+2)) = 0

3*5*x*(4*x+2)+3*8*(2*x+1)-8*(2*x+1)*(4*x+2) = 0

60*x^2-64*x^2+78*x-64*x-16+24 = 0

14*x-4*x^2+8 = 0

14*x-4*x^2+8 = 0

2*(7*x-2*x^2+4) = 0

7*x-2*x^2+4 = 0

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

DELTA = 81

DELTA > 0

x = (81^(1/2)-7)/(-2*2) or x = (-81^(1/2)-7)/(-2*2)

x = -1/2 or x = 4

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

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

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

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

( x+1/2 )

x+1/2 = 0 // - 1/2

x = -1/2

( x-4 )

x-4 = 0 // + 4

x = 4

x in { -1/2} 

x = 4

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