Question 152495


{{{(3)/(x+3)=(3)/(4x)+(25)/(8)}}} Start with the given equation.



{{{8x*cross(x+3)((3)/cross(x+3))=8x(x+3)((3)/cross(4x))+cross(8)x(x+3)((25)/cross(8))}}} Multiply <font size="4"><b>every</b></font> term on both sides by the LCD {{{8x(x+3)}}}. Doing this will eliminate all of the fractions.



{{{24x=6(x+3)+25x(x+3)}}} Simplify



{{{24x=6x+18+25x^2+75x}}} Distribute



{{{24x=6x+18+25x^2+75x}}} Start with the given equation.



{{{0=-24x+6x+18+25x^2+75x}}} Get all terms to the left side.



{{{0=25x^2+57x+18}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=25}}}, {{{b=57}}}, and {{{c=18}}}



Let's use the quadratic formula to solve for x



{{{x = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{x = (-(57) +- sqrt( (57)^2-4(25)(18) ))/(2(25))}}} Plug in  {{{a=25}}}, {{{b=57}}}, and {{{c=18}}}



{{{x = (-57 +- sqrt( 3249-4(25)(18) ))/(2(25))}}} Square {{{57}}} to get {{{3249}}}. 



{{{x = (-57 +- sqrt( 3249-1800 ))/(2(25))}}} Multiply {{{4(25)(18)}}} to get {{{1800}}}



{{{x = (-57 +- sqrt( 1449 ))/(2(25))}}} Subtract {{{1800}}} from {{{3249}}} to get {{{1449}}}



{{{x = (-57 +- sqrt( 1449 ))/(50)}}} Multiply {{{2}}} and {{{25}}} to get {{{50}}}. 



{{{x = (-57 +- 3*sqrt(161))/(50)}}} Simplify the square root  (note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  



{{{x = (-57+3*sqrt(161))/(50)}}} or {{{x = (-57-3*sqrt(161))/(50)}}} Break up the expression.  



So our answers are {{{x = (-57+3*sqrt(161))/(50)}}} or {{{x = (-57-3*sqrt(161))/(50)}}} 



which approximate to {{{x=-0.379}}} or {{{x=-1.901}}}