Question 604229
{{{ y - 3/y + 8 = 1/5 }}}
Multiply both sides by {{{ 5y }}}
{{{ 5y^2 - 15 + 40y = y }}}
{{{ 5y^2 + 39y - 15 = 0 }}}
Use quadratic formula
{{{ y = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 5 }}}
{{{ b = 39 }}}
{{{ c = -15 }}}
{{{ y = (-39 +- sqrt( 39^2 - 4*5*(-15) )) / (2*5) }}}
{{{ y = (-39 +- sqrt( 1521 + 300 )) / 10 }}}
{{{ y = (-39 +- sqrt( 1821 )) / 10 }}}
{{{ y = (-39 + 42.673) / 10 }}}
{{{ y = 3.673 / 10 }}}
{{{ y = .3673 }}}
and also
{{{ y = (-39 - 42.673) / 10 }}}
{{{ y = -81.673 / 10 }}}
{{{ y = -8.1673 }}}
Both answers should solve the equation
check:
{{{ y - 3/y + 8 = 1/5 }}}
{{{ -8.1673 - 3/(-8.1673) + 8 = .2 }}}
{{{ -8.1673 + .36732 + 8 = .2 }}}
{{{ -.1673 + .3673 = .2 }}}
{{{ .2 = .2 }}}
OK
You can check the other answer