Question 338387
I'm assuming that the equation is {{{x/3=4/(x+1)}}}



{{{x/3=4/(x+1)}}} Start with the given equation.



{{{x(x+1)=4*3}}} Cross multiply.



{{{x(x+1)=12}}} Multiply



{{{x^2+x=12}}} Distribute.



{{{x^2+x-12=0}}} Subtract 12 from both sides.



Notice that the quadratic {{{x^2+x-12}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=1}}}, and {{{C=-12}}}



Let's use the quadratic formula to solve for "x":



{{{x = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{x = (-(1) +- sqrt( (1)^2-4(1)(-12) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=1}}}, and {{{C=-12}}}



{{{x = (-1 +- sqrt( 1-4(1)(-12) ))/(2(1))}}} Square {{{1}}} to get {{{1}}}. 



{{{x = (-1 +- sqrt( 1--48 ))/(2(1))}}} Multiply {{{4(1)(-12)}}} to get {{{-48}}}



{{{x = (-1 +- sqrt( 1+48 ))/(2(1))}}} Rewrite {{{sqrt(1--48)}}} as {{{sqrt(1+48)}}}



{{{x = (-1 +- sqrt( 49 ))/(2(1))}}} Add {{{1}}} to {{{48}}} to get {{{49}}}



{{{x = (-1 +- sqrt( 49 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-1 +- 7)/(2)}}} Take the square root of {{{49}}} to get {{{7}}}. 



{{{x = (-1 + 7)/(2)}}} or {{{x = (-1 - 7)/(2)}}} Break up the expression. 



{{{x = (6)/(2)}}} or {{{x =  (-8)/(2)}}} Combine like terms. 



{{{x = 3}}} or {{{x = -4}}} Simplify. 



So the solutions are {{{x = 3}}} or {{{x = -4}}} 



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