(6x^2-x-12)/(2x-3)

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Solution for (6x^2-x-12)/(2x-3) equation: 


D( x )

2*x-3 = 0

2*x-3 = 0

2*x-3 = 0

2*x-3 = 0 // + 3

2*x = 3 // : 2

x = 3/2

x in (-oo:3/2) U (3/2:+oo)

(6*x^2-x-12)/(2*x-3) = 0

6*x^2-x-12 = 0

6*x^2-x-12 = 0

DELTA = (-1)^2-(-12*4*6)

DELTA = 289

DELTA > 0

x = (289^(1/2)+1)/(2*6) or x = (1-289^(1/2))/(2*6)

x = 3/2 or x = -4/3

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

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

( x+4/3 )

x+4/3 = 0 // - 4/3

x = -4/3

( x-3/2 )

x-3/2 = 0 // + 3/2

x = 3/2

x in { 3/2} 

x = -4/3

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