Question 307388
{{{ (4a-3)= (a+33)/(a+1) }}} Start with the given equation.



{{{ (4a-3)(a+1)= a+33 }}} Multiply both sides by {{{a+1}}}.



{{{ 4a^2+a-3= a+33 }}} FOIL



{{{4a^2+a-3-a-33=0}}} Get every term to the left side.



{{{4a^2+0a-36=0}}} Combine like terms.



Notice that the quadratic {{{4a^2+0a-36}}} is in the form of {{{Aa^2+Ba+C}}} where {{{A=4}}}, {{{B=0}}}, and {{{C=-36}}}



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



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



{{{a = (0 +- sqrt( (0)^2-4(4)(-36) ))/(2(4))}}} Plug in  {{{A=4}}}, {{{B=0}}}, and {{{C=-36}}}



{{{a = (0 +- sqrt( 0-4(4)(-36) ))/(2(4))}}} Square {{{0}}} to get {{{0}}}. 



{{{a = (0 +- sqrt( 0--576 ))/(2(4))}}} Multiply {{{4(4)(-36)}}} to get {{{-576}}}



{{{a = (0 +- sqrt( 0+576 ))/(2(4))}}} Rewrite {{{sqrt(0--576)}}} as {{{sqrt(0+576)}}}



{{{a = (0 +- sqrt( 576 ))/(2(4))}}} Add {{{0}}} to {{{576}}} to get {{{576}}}



{{{a = (0 +- sqrt( 576 ))/(8)}}} Multiply {{{2}}} and {{{4}}} to get {{{8}}}. 



{{{a = (0 +- 24)/(8)}}} Take the square root of {{{576}}} to get {{{24}}}. 



{{{a = (0 + 24)/(8)}}} or {{{a = (-0 - 24)/(8)}}} Break up the expression. 



{{{a = (24)/(8)}}} or {{{a =  (-24)/(8)}}} Combine like terms. 



{{{a = 3}}} or {{{a = -3}}} Simplify. 



So the solutions are {{{a = 3}}} or {{{a = -3}}}