Question 263253


{{{9x^2+21x-8=0}}} Start with the given equation.



Notice that the quadratic {{{9x^2+21x-8}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=9}}}, {{{B=21}}}, and {{{C=-8}}}



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



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



{{{x = (-(21) +- sqrt( (21)^2-4(9)(-8) ))/(2(9))}}} Plug in  {{{A=9}}}, {{{B=21}}}, and {{{C=-8}}}



{{{x = (-21 +- sqrt( 441-4(9)(-8) ))/(2(9))}}} Square {{{21}}} to get {{{441}}}. 



{{{x = (-21 +- sqrt( 441--288 ))/(2(9))}}} Multiply {{{4(9)(-8)}}} to get {{{-288}}}



{{{x = (-21 +- sqrt( 441+288 ))/(2(9))}}} Rewrite {{{sqrt(441--288)}}} as {{{sqrt(441+288)}}}



{{{x = (-21 +- sqrt( 729 ))/(2(9))}}} Add {{{441}}} to {{{288}}} to get {{{729}}}



{{{x = (-21 +- sqrt( 729 ))/(18)}}} Multiply {{{2}}} and {{{9}}} to get {{{18}}}. 



{{{x = (-21 +- 27)/(18)}}} Take the square root of {{{729}}} to get {{{27}}}. 



{{{x = (-21 + 27)/(18)}}} or {{{x = (-21 - 27)/(18)}}} Break up the expression. 



{{{x = (6)/(18)}}} or {{{x =  (-48)/(18)}}} Combine like terms. 



{{{x = 1/3}}} or {{{x = -8/3}}} Simplify. 



So the solutions are {{{x = 1/3}}} or {{{x = -8/3}}}