(4x^2-10x-24)/(2x+3)

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Solution for (4x^2-10x-24)/(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)

(4*x^2-(10*x)-24)/(2*x+3) = 0

(4*x^2-10*x-24)/(2*x+3) = 0

4*x^2-10*x-24 = 0

2*(2*x^2-5*x-12) = 0

2*x^2-5*x-12 = 0

DELTA = (-5)^2-(-12*2*4)

DELTA = 121

DELTA > 0

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

x = 4 or x = -3/2

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

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

( x+3/2 )

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

x = -3/2

( x-4 )

x-4 = 0 // + 4

x = 4

x in { -3/2} 

x = 4

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