```Question 152495

{{{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

{{{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 = (-(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}}} ```