(8x^2-10x-12)/(4x-3)

Solution for (8x^2-10x-12)/(4x-3) equation:

D( x )

4*x-3 = 0

4*x-3 = 0

4*x-3 = 0

4*x-3 = 0 // + 3

4*x = 3 // : 4

x = 3/4

x in (-oo:3/4) U (3/4:+oo)

(8*x^2-(10*x)-12)/(4*x-3) = 0

(8*x^2-10*x-12)/(4*x-3) = 0

8*x^2-10*x-12 = 0

2*(4*x^2-5*x-6) = 0

4*x^2-5*x-6 = 0

DELTA = (-5)^2-(-6*4*4)

DELTA = 121

DELTA > 0

x = (121^(1/2)+5)/(2*4) or x = (5-121^(1/2))/(2*4)

x = 2 or x = -3/4

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

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

( 2 )

2 = 0

x belongs to the empty set

( x+3/4 )

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

x = -3/4

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -3/4, 2 }