(3x+2)/(2x-1)=(x-10)/(x-7)

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Solution for (3x+2)/(2x-1)=(x-10)/(x-7) equation: 


D( x )

x-7 = 0

2*x-1 = 0

x-7 = 0

x-7 = 0

x-7 = 0 // + 7

x = 7

2*x-1 = 0

2*x-1 = 0

2*x-1 = 0 // + 1

2*x = 1 // : 2

x = 1/2

x in (-oo:1/2) U (1/2:7) U (7:+oo)

(3*x+2)/(2*x-1) = (x-10)/(x-7) // - (x-10)/(x-7)

(3*x+2)/(2*x-1)-((x-10)/(x-7)) = 0

(3*x+2)/(2*x-1)+(-1*(x-10))/(x-7) = 0

((3*x+2)*(x-7))/((2*x-1)*(x-7))+(-1*(x-10)*(2*x-1))/((2*x-1)*(x-7)) = 0

(3*x+2)*(x-7)-1*(x-10)*(2*x-1) = 0

x^2+2*x-24 = 0

x^2+2*x-24 = 0

x^2+2*x-24 = 0

DELTA = 2^2-(-24*1*4)

DELTA = 100

DELTA > 0

x = (100^(1/2)-2)/(1*2) or x = (-100^(1/2)-2)/(1*2)

x = 4 or x = -6

(x+6)*(x-4) = 0

((x+6)*(x-4))/((2*x-1)*(x-7)) = 0

((x+6)*(x-4))/((2*x-1)*(x-7)) = 0 // * (2*x-1)*(x-7)

(x+6)*(x-4) = 0

( x+6 )

x+6 = 0 // - 6

x = -6

( x-4 )

x-4 = 0 // + 4

x = 4

x in { -6, 4 }

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