((x-5)/(3x))+(6/(2x-1))=0

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Solution for ((x-5)/(3x))+(6/(2x-1))=0 equation:


D( x )

3*x = 0

2*x-1 = 0

3*x = 0

3*x = 0

3*x = 0 // : 3

x = 0

2*x-1 = 0

2*x-1 = 0

2*x-1 = 0 // + 1

2*x = 1 // : 2

x = 1/2

x in (-oo:0) U (0:1/2) U (1/2:+oo)

(x-5)/(3*x)+6/(2*x-1) = 0

((x-5)*(2*x-1))/(3*x*(2*x-1))+(3*6*x)/(3*x*(2*x-1)) = 0

(x-5)*(2*x-1)+3*6*x = 0

2*x^2+7*x+5 = 0

2*x^2+7*x+5 = 0

2*x^2+7*x+5 = 0

DELTA = 7^2-(2*4*5)

DELTA = 9

DELTA > 0

x = (9^(1/2)-7)/(2*2) or x = (-9^(1/2)-7)/(2*2)

x = -1 or x = -5/2

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

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

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

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

( x+1 )

x+1 = 0 // - 1

x = -1

( x+5/2 )

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

x = -5/2

x in { -1, -5/2 }

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