Question 332295


{{{15x^2+36=-48x}}} Start with the given equation.



{{{15x^2+48x+36=0}}} Add 48x to both sides.



Notice that the quadratic {{{15x^2+48x+36}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=15}}}, {{{B=48}}}, and {{{C=36}}}



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



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



{{{x = (-(48) +- sqrt( (48)^2-4(15)(36) ))/(2(15))}}} Plug in  {{{A=15}}}, {{{B=48}}}, and {{{C=36}}}



{{{x = (-48 +- sqrt( 2304-4(15)(36) ))/(2(15))}}} Square {{{48}}} to get {{{2304}}}. 



{{{x = (-48 +- sqrt( 2304-2160 ))/(2(15))}}} Multiply {{{4(15)(36)}}} to get {{{2160}}}



{{{x = (-48 +- sqrt( 144 ))/(2(15))}}} Subtract {{{2160}}} from {{{2304}}} to get {{{144}}}



{{{x = (-48 +- sqrt( 144 ))/(30)}}} Multiply {{{2}}} and {{{15}}} to get {{{30}}}. 



{{{x = (-48 +- 12)/(30)}}} Take the square root of {{{144}}} to get {{{12}}}. 



{{{x = (-48 + 12)/(30)}}} or {{{x = (-48 - 12)/(30)}}} Break up the expression. 



{{{x = (-36)/(30)}}} or {{{x =  (-60)/(30)}}} Combine like terms. 



{{{x = -6/5}}} or {{{x = -2}}} Simplify. 



So the solutions are {{{x = -6/5}}} or {{{x = -2}}}