(-7/(4v+20))+2=7/(v+5)

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Solution for (-7/(4v+20))+2=7/(v+5) equation: 


D( v )

4*v+20 = 0

v+5 = 0

4*v+20 = 0

4*v+20 = 0

4*v+20 = 0 // - 20

4*v = -20 // : 4

v = -20/4

v = -5

v+5 = 0

v+5 = 0

v+5 = 0 // - 5

v = -5

v in (-oo:-5) U (-5:+oo)

2-7/(4*v+20) = 7/(v+5) // - 7/(v+5)

2-7/(4*v+20)-(7/(v+5)) = 0

2-7/(4*v+20)-7*(v+5)^-1 = 0

2-7/(4*v+20)-7/(v+5) = 0

(-7*(v+5))/((4*v+20)*(v+5))+(-7*(4*v+20))/((4*v+20)*(v+5))+(2*(4*v+20)*(v+5))/((4*v+20)*(v+5)) = 0

2*(4*v+20)*(v+5)-7*(v+5)-7*(4*v+20) = 0

8*v^2-35*v+80*v-175+200 = 0

8*v^2+45*v+25 = 0

8*v^2+45*v+25 = 0

8*v^2+45*v+25 = 0

DELTA = 45^2-(4*8*25)

DELTA = 1225

DELTA > 0

v = (1225^(1/2)-45)/(2*8) or v = (-1225^(1/2)-45)/(2*8)

v = -5/8 or v = -5

(v+5)*(v+5/8) = 0

((v+5)*(v+5/8))/((4*v+20)*(v+5)) = 0

((v+5)*(v+5/8))/((4*v+20)*(v+5)) = 0 // * (4*v+20)*(v+5)

(v+5)*(v+5/8) = 0

( v+5/8 )

v+5/8 = 0 // - 5/8

v = -5/8

( v+5 )

v+5 = 0 // - 5

v = -5

v in { -5} 

v = -5/8

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