0.1=(2/(400+y))-(8/y)

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Solution for 0.1=(2/(400+y))-(8/y) equation:


D( y )

y = 0

y+400 = 0

y = 0

y = 0

y+400 = 0

y+400 = 0

y+400 = 0 // - 400

y = -400

y in (-oo:-400) U (-400:0) U (0:+oo)

0.1 = 2/(y+400)-(8/y) // - 2/(y+400)-(8/y)

8/y-(2/(y+400))+0.1 = 0

8/y-2*(y+400)^-1+0.1 = 0

8/y-2/(y+400)+0.1 = 0

(-2*y)/(y*(y+400))+(8*(y+400))/(y*(y+400))+(0.1*y*(y+400))/(y*(y+400)) = 0

8*(y+400)+0.1*y*(y+400)-2*y = 0

0.1*y^2+6*y+40*y+3200 = 0

0.1*y^2+46*y+3200 = 0

0.1*y^2+46*y+3200 = 0

0.1*y^2+46*y+3200 = 0

DELTA = 46^2-(0.1*4*3200)

DELTA = 836

DELTA > 0

y = (836^(1/2)-46)/(0.1*2) or y = (-836^(1/2)-46)/(0.1*2)

y = 5*(2*209^(1/2)-46) or y = 5*(-2*209^(1/2)-46)

(y-5*(-2*209^(1/2)-46))*(y-5*(2*209^(1/2)-46)) = 0

((y-5*(-2*209^(1/2)-46))*(y-5*(2*209^(1/2)-46)))/(y*(y+400)) = 0

((y-5*(-2*209^(1/2)-46))*(y-5*(2*209^(1/2)-46)))/(y*(y+400)) = 0 // * y*(y+400)

(y-5*(-2*209^(1/2)-46))*(y-5*(2*209^(1/2)-46)) = 0

( y-5*(-2*209^(1/2)-46) )

y-5*(-2*209^(1/2)-46) = 0 // + -5*(-2*209^(1/2)-46)

y = -(-5*(-2*209^(1/2)-46))

y = 5*(-2*209^(1/2)-46)

( y-5*(2*209^(1/2)-46) )

y-5*(2*209^(1/2)-46) = 0 // + -5*(2*209^(1/2)-46)

y = -(-5*(2*209^(1/2)-46))

y = 5*(2*209^(1/2)-46)

y in { 5*(-2*209^(1/2)-46), 5*(2*209^(1/2)-46) }

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