Question 210159

{{{3x^2-7x-6=0}}} Start with the given equation.



Notice that the quadratic {{{3x^2-7x-6}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=3}}}, {{{B=-7}}}, and {{{C=-6}}}



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



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



{{{x = (-(-7) +- sqrt( (-7)^2-4(3)(-6) ))/(2(3))}}} Plug in  {{{A=3}}}, {{{B=-7}}}, and {{{C=-6}}}



{{{x = (7 +- sqrt( (-7)^2-4(3)(-6) ))/(2(3))}}} Negate {{{-7}}} to get {{{7}}}. 



{{{x = (7 +- sqrt( 49-4(3)(-6) ))/(2(3))}}} Square {{{-7}}} to get {{{49}}}. 



{{{x = (7 +- sqrt( 49--72 ))/(2(3))}}} Multiply {{{4(3)(-6)}}} to get {{{-72}}}



{{{x = (7 +- sqrt( 49+72 ))/(2(3))}}} Rewrite {{{sqrt(49--72)}}} as {{{sqrt(49+72)}}}



{{{x = (7 +- sqrt( 121 ))/(2(3))}}} Add {{{49}}} to {{{72}}} to get {{{121}}}



{{{x = (7 +- sqrt( 121 ))/(6)}}} Multiply {{{2}}} and {{{3}}} to get {{{6}}}. 



{{{x = (7 +- 11)/(6)}}} Take the square root of {{{121}}} to get {{{11}}}. 



{{{x = (7 + 11)/(6)}}} or {{{x = (7 - 11)/(6)}}} Break up the expression. 



{{{x = (18)/(6)}}} or {{{x =  (-4)/(6)}}} Combine like terms. 



{{{x = 3}}} or {{{x = -2/3}}} Simplify. 



So the solutions are {{{x = 3}}} or {{{x = -2/3}}}