Question 765245
{{{10/(2x) + 4/(x-5)= 4}}}.......common denominator


{{{10(x-5)/((x-5)(2x)) + (4*2x)/(2x(x-5))= 4}}}

{{{(10(x-5) + 8x)/(2x(x-5))= 4}}}

{{{(10x-50 + 8x)/(2x^2-10x)= 4}}}

{{{(18x-50)/(2x^2-10x)= 4}}}

{{{(18x-50)= 4(2x^2-10x)}}}

{{{18x-50= 8x^2-40x}}}

{{{0= 8x^2-18x-40x+50}}}

{{{ 8x^2-58x+50=0}}}....divide all terms by {{{2}}}

{{{ 4x^2-29x+25=0}}}...use quadratic formula to solve for {{{x}}}


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


{{{x = (-(-29) +- sqrt( (-29)^2-4*4*25 ))/(2*4) }}}


{{{x = (29 +- sqrt( 841-400 ))/8 }}}


{{{x = (29 +- sqrt( 441 ))/8 }}}


{{{x = (29 +- 21)/8 }}}

solutions:

{{{x = (29 + 21)/8 }}}

{{{x = 50/8 }}}

{{{x = 25/4 }}}

{{{highlight(x = 6.25) }}}


or

{{{x = (29 - 21)/8 }}}

{{{x = 8/8 }}}

{{{highlight(x = 1) }}}