Question 200964
{{{9x -2 = 3x^2}}} Start with the given equation.



{{{0 = 3x^2-9x+2}}} Get everything to one side



Notice that the quadratic {{{3x^2-9x+2}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=3}}}, {{{B=-9}}}, and {{{C=2}}}



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



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



{{{x = (-(-9) +- sqrt( (-9)^2-4(3)(2) ))/(2(3))}}} Plug in  {{{A=3}}}, {{{B=-9}}}, and {{{C=2}}}



{{{x = (9 +- sqrt( (-9)^2-4(3)(2) ))/(2(3))}}} Negate {{{-9}}} to get {{{9}}}. 



{{{x = (9 +- sqrt( 81-4(3)(2) ))/(2(3))}}} Square {{{-9}}} to get {{{81}}}. 



{{{x = (9 +- sqrt( 81-24 ))/(2(3))}}} Multiply {{{4(3)(2)}}} to get {{{24}}}



{{{x = (9 +- sqrt( 57 ))/(2(3))}}} Subtract {{{24}}} from {{{81}}} to get {{{57}}}



{{{x = (9 +- sqrt( 57 ))/(6)}}} Multiply {{{2}}} and {{{3}}} to get {{{6}}}. 



{{{x = (9+sqrt(57))/(6)}}} or {{{x = (9-sqrt(57))/(6)}}} Break up the expression.  



So the solutions are {{{x = (9+sqrt(57))/(6)}}} or {{{x = (9-sqrt(57))/(6)}}} 



which approximate to {{{x=2.758}}} or {{{x=0.242}}}