Question 266442
{{{4x(x-9)-5x(x-8)=-5}}} Start with the given equation.



{{{4x^2-36x-5x^2+40x+5=0}}} Add 5 to both sides.



{{{-x^2+4x+5=0}}} Combine like terms.



Notice that the quadratic {{{-x^2+4x+5}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=-1}}}, {{{B=4}}}, and {{{C=5}}}



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



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



{{{x = (-(4) +- sqrt( (4)^2-4(-1)(5) ))/(2(-1))}}} Plug in  {{{A=-1}}}, {{{B=4}}}, and {{{C=5}}}



{{{x = (-4 +- sqrt( 16-4(-1)(5) ))/(2(-1))}}} Square {{{4}}} to get {{{16}}}. 



{{{x = (-4 +- sqrt( 16--20 ))/(2(-1))}}} Multiply {{{4(-1)(5)}}} to get {{{-20}}}



{{{x = (-4 +- sqrt( 16+20 ))/(2(-1))}}} Rewrite {{{sqrt(16--20)}}} as {{{sqrt(16+20)}}}



{{{x = (-4 +- sqrt( 36 ))/(2(-1))}}} Add {{{16}}} to {{{20}}} to get {{{36}}}



{{{x = (-4 +- sqrt( 36 ))/(-2)}}} Multiply {{{2}}} and {{{-1}}} to get {{{-2}}}. 



{{{x = (-4 +- 6)/(-2)}}} Take the square root of {{{36}}} to get {{{6}}}. 



{{{x = (-4 + 6)/(-2)}}} or {{{x = (-4 - 6)/(-2)}}} Break up the expression. 



{{{x = (2)/(-2)}}} or {{{x =  (-10)/(-2)}}} Combine like terms. 



{{{x = -1}}} or {{{x = 5}}} Reduce. 



So the solutions are {{{x = -1}}} or {{{x = 5}}}