Question 402500
{{{5/9w + 8/9 = 3w }}}.........first, find common denominator for left side; for {{{9w}}} and {{{9}}} it is {{{9w}}}...multiply both sides by  {{{9w}}}


{{{9w(5/9w) + 9w(8/9) = 3w*9w }}}


{{{cross(9w)(5/cross(9w)) + cross(9)w(8/cross(9)) = 27w^2 }}}


{{{5+ 8w = 27w^2 }}}


{{{27w^2 -8w - 5 = 0}}}.......use quadratic formula to solve for {{{w}}}


{{{w = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


{{{w = (-(-8) +- sqrt( (-8)^2-4*27*(-5) ))/(2*27) }}}


{{{w = (8 +- sqrt( 64 -108*(-5) ))/(54) }}}


{{{w = (8 +- sqrt( 64 + 540 ))/(54) }}}


{{{w = (8 +- sqrt( 604))/(54) }}}


{{{w = (8 +- ( 24.6))/(54) }}}


first solution:


{{{w1 = (8 + ( 24.6))/(54) }}}

{{{w1 = ( 32.6)/54 }}}

{{{w1 =  0.6 }}}


second solution:

{{{w2 = (8 - ( 24.6))/(54) }}}


{{{w2 = ( -16.6)/54 }}}


{{{w2 = - 0.3 }}}


check: if {{{w1 =  0.6 }}}


{{{5/9w + 8/9 = 3w }}}


{{{5/(9(0.6)) + 8/9 = 3(0.6) }}}


{{{5/(5.4) +0.9 = 1.8 }}}


{{{0.9 + 0.9 = 1.8 }}}


{{{1.8 = 1.8 }}}