Question 191981
You're on the right track, you just need to solve the equation {{{0=x^2+10x-240}}}



{{{0=x^2+10x-240}}} Start with the given equation.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=10}}}, and {{{c=-240}}}



Let's use the quadratic formula to solve for x



{{{x = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{x = (-(10) +- sqrt( (10)^2-4(1)(-240) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=10}}}, and {{{c=-240}}}



{{{x = (-10 +- sqrt( 100-4(1)(-240) ))/(2(1))}}} Square {{{10}}} to get {{{100}}}. 



{{{x = (-10 +- sqrt( 100--960 ))/(2(1))}}} Multiply {{{4(1)(-240)}}} to get {{{-960}}}



{{{x = (-10 +- sqrt( 100+960 ))/(2(1))}}} Rewrite {{{sqrt(100--960)}}} as {{{sqrt(100+960)}}}



{{{x = (-10 +- sqrt( 1060 ))/(2(1))}}} Add {{{100}}} to {{{960}}} to get {{{1060}}}



{{{x = (-10 +- sqrt( 1060 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-10 +- 2*sqrt(265))/(2)}}} Simplify the square root  (note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  



{{{x = (-10)/(2) +- (2*sqrt(265))/(2)}}} Break up the fraction.  



{{{x = -5 +- 1*sqrt(265)}}} Reduce.  



{{{x = -5+sqrt(265)}}} or {{{x = -5-sqrt(265)}}} Break up the expression.  



So the answers are {{{x = -5+sqrt(265)}}} or {{{x = -5-sqrt(265)}}} 



which approximate to {{{x=11.279}}} or {{{x=-21.279}}} 




However since "x" is a speed and a negative speed doesn't make sense, this means that the only answer is {{{x = 11.279}}}



So her speed before lunch was approximately 11.279 mph and her speed after lunch was about 7.279 mph