Question 540548
{{{3x^2-5x-8=0}}} Start with the given equation.



Notice that the quadratic {{{3x^2-5x-8}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=3}}}, {{{B=-5}}}, 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 = (-(-5) +- sqrt( (-5)^2-4(3)(-8) ))/(2(3))}}} Plug in  {{{A=3}}}, {{{B=-5}}}, and {{{C=-8}}}



{{{x = (5 +- sqrt( (-5)^2-4(3)(-8) ))/(2(3))}}} Negate {{{-5}}} to get {{{5}}}. 



{{{x = (5 +- sqrt( 25-4(3)(-8) ))/(2(3))}}} Square {{{-5}}} to get {{{25}}}. 



{{{x = (5 +- sqrt( 25--96 ))/(2(3))}}} Multiply {{{4(3)(-8)}}} to get {{{-96}}}



{{{x = (5 +- sqrt( 25+96 ))/(2(3))}}} Rewrite {{{sqrt(25--96)}}} as {{{sqrt(25+96)}}}



{{{x = (5 +- sqrt( 121 ))/(2(3))}}} Add {{{25}}} to {{{96}}} to get {{{121}}}



{{{x = (5 +- sqrt( 121 ))/(6)}}} Multiply {{{2}}} and {{{3}}} to get {{{6}}}. 



{{{x = (5 +- 11)/(6)}}} Take the square root of {{{121}}} to get {{{11}}}. 



{{{x = (5 + 11)/(6)}}} or {{{x = (5 - 11)/(6)}}} Break up the expression. 



{{{x = (16)/(6)}}} or {{{x =  (-6)/(6)}}} Combine like terms. 



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



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



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