((x^2-9)/4)/((3-x)/8)=10

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Solution for ((x^2-9)/4)/((3-x)/8)=10 equation: 


D( x )

(3-x)/8 = 0

(3-x)/8 = 0

(3-x)/8 = 0

3-x = 0 // - 3

-x = -3 // * -1

x = 3

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

((x^2-9)/4)/((3-x)/8) = 10 // - 10

((x^2-9)/4)/((3-x)/8)-10 = 0

(8*(x^2-9))/(4*(3-x))-10 = 0

(8*(x^2-9))/(4*(3-x))+(-10*4*(3-x))/(4*(3-x)) = 0

8*(x^2-9)-10*4*(3-x) = 0

8*x^2+40*x-192 = 0

8*x^2+40*x-192 = 0

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

x^2+5*x-24 = 0

DELTA = 5^2-(-24*1*4)

DELTA = 121

DELTA > 0

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

x = 3 or x = -8

8*(x+8)*(x-3) = 0

(8*(x+8)*(x-3))/(4*(3-x)) = 0

(8*(x+8)*(x-3))/(4*(3-x)) = 0 // * 4*(3-x)

8*(x+8)*(x-3) = 0

( 8 )

8 = 0

x belongs to the empty set

( x+8 )

x+8 = 0 // - 8

x = -8

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 3} 

x = -8

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