5x^2+20x/(x+4)(x-6)

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Solution for 5x^2+20x/(x+4)(x-6) equation: 


D( x )

x+4 = 0

x+4 = 0

x+4 = 0

x+4 = 0 // - 4

x = -4

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

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

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

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

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

5*x^3+40*x^2-120*x = 0

5*x^3+40*x^2-120*x = 0

5*x*(x^2+8*x-24) = 0

x^2+8*x-24 = 0

DELTA = 8^2-(-24*1*4)

DELTA = 160

DELTA > 0

x = (160^(1/2)-8)/(1*2) or x = (-160^(1/2)-8)/(1*2)

x = (4*10^(1/2)-8)/2 or x = (-4*10^(1/2)-8)/2

5*x*(x-((-4*10^(1/2)-8)/2))*(x-((4*10^(1/2)-8)/2)) = 0

(5*x*(x-((-4*10^(1/2)-8)/2))*(x-((4*10^(1/2)-8)/2)))/(x+4) = 0

(5*x*(x-((-4*10^(1/2)-8)/2))*(x-((4*10^(1/2)-8)/2)))/(x+4) = 0 // * x+4

5*x*(x-((-4*10^(1/2)-8)/2))*(x-((4*10^(1/2)-8)/2)) = 0

( 5*x )

5*x = 0 // : 5

x = 0

( x-((-4*10^(1/2)-8)/2) )

x-((-4*10^(1/2)-8)/2) = 0 // + (-4*10^(1/2)-8)/2

x = (-4*10^(1/2)-8)/2

( x-((4*10^(1/2)-8)/2) )

x-((4*10^(1/2)-8)/2) = 0 // + (4*10^(1/2)-8)/2

x = (4*10^(1/2)-8)/2

x in { 0, (-4*10^(1/2)-8)/2, (4*10^(1/2)-8)/2 }

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