Question 303850


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



Notice that the quadratic {{{-3x^2+7x}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=-3}}}, {{{B=7}}}, and {{{C=0}}}



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)(0) ))/(2(-3))}}} Plug in  {{{A=-3}}}, {{{B=7}}}, and {{{C=0}}}



{{{x = (-7 +- sqrt( 49-4(-3)(0) ))/(2(-3))}}} Square {{{7}}} to get {{{49}}}. 



{{{x = (-7 +- sqrt( 49-0 ))/(2(-3))}}} Multiply {{{4(-3)(0)}}} to get {{{0}}}



{{{x = (-7 +- sqrt( 49 ))/(2(-3))}}} Subtract {{{0}}} from {{{49}}} to get {{{49}}}



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



{{{x = (-7 +- 7)/(-6)}}} Take the square root of {{{49}}} to get {{{7}}}. 



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



{{{x = (0)/(-6)}}} or {{{x =  (-14)/(-6)}}} Combine like terms. 



{{{x = 0}}} or {{{x = 7/3}}} Simplify. 



So the solutions are {{{x = 0}}} or {{{x = 7/3}}}