Question 764517
{{{6/x+8/(x+5)=3}}}....common denominator

{{{6/(x(x+5))+8/(x(x+5))=3}}}

{{{(6(x+5)+8x)/(x(x+5))=3}}}

{{{6(x+5)+8x=3(x(x+5))}}}

{{{6x+30+8x=3(x^2+5x)}}}

{{{14x+30=3x^2+15x}}}

{{{0=3x^2+15x-14x-30}}}

{{{3x^2+x-30=0}}}


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


{{{x = (-1 +- sqrt( 1^2-4*3*(-30) ))/(2*3) }}} 

{{{x = (-1 +- sqrt( 1+360 ))/6 }}}

{{{x = (-1 +- sqrt( 361 ))/6 }}}

{{{x = (-1 +-19)/6 }}}

solutions:

{{{x = (-1 +19)/6 }}}

{{{x = 18/6 }}}

{{{x = 3}}}

or

{{{x = (-1 -19)/6 }}}

{{{x = -20/6 }}}

{{{x = -3.33}}}

so, you have two real solutions:{{{x = 3}}} and {{{x = -3.33}}}



 {{{ graph( 600, 600, -10, 10, -40, 10, 3x^2+x-30) }}}