(8x^3-10x^2-25x)/(4x^2+5x)=0

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Solution for (8x^3-10x^2-25x)/(4x^2+5x)=0 equation: 


D( x )

4*x^2+5*x = 0

4*x^2+5*x = 0

4*x^2+5*x = 0

4*x^2+5*x = 0

DELTA = 5^2-(0*4*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)-5)/(2*4) or x = (-25^(1/2)-5)/(2*4)

x = 0 or x = -5/4

x in (-oo:-5/4) U (-5/4:0) U (0:+oo)

(8*x^3-(10*x^2)-(25*x))/(4*x^2+5*x) = 0

(8*x^3-10*x^2-25*x)/(4*x^2+5*x) = 0

8*x^3-10*x^2-25*x = 0

x*(8*x^2-10*x-25) = 0

8*x^2-10*x-25 = 0

DELTA = (-10)^2-(-25*4*8)

DELTA = 900

DELTA > 0

x = (900^(1/2)+10)/(2*8) or x = (10-900^(1/2))/(2*8)

x = 5/2 or x = -5/4

x*(x+5/4)*(x-5/2) = 0

4*x^2+5*x = 0

x*(4*x+5) = 0

4*x+5 = 0 // - 5

4*x = -5 // : 4

x = -5/4

x*(x+5/4) = 0

(x*(x+5/4)*(x-5/2))/(x*(x+5/4)) = 0

( x+5/4 )

x+5/4 = 0 // - 5/4

x = -5/4

( x-5/2 )

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

x = 5/2

( x )

x = 0

x in { -5/4} 

x in { 0} 

x = 5/2

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