Question 202429
I'm not sure that you have the right equation (I don't have access to the drawing), but here's how you would solve it.





{{{x^2+3x=-10x+140}}} Start with the given equation.



{{{x^2+3x+10x-140=0}}} Get all terms to the left side.



{{{x^2+13x-140=0}}} Combine like terms.



Notice that the quadratic {{{x^2+13x-140}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=13}}}, and {{{C=-140}}}



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



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



{{{x = (-(13) +- sqrt( (13)^2-4(1)(-140) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=13}}}, and {{{C=-140}}}



{{{x = (-13 +- sqrt( 169-4(1)(-140) ))/(2(1))}}} Square {{{13}}} to get {{{169}}}. 



{{{x = (-13 +- sqrt( 169--560 ))/(2(1))}}} Multiply {{{4(1)(-140)}}} to get {{{-560}}}



{{{x = (-13 +- sqrt( 169+560 ))/(2(1))}}} Rewrite {{{sqrt(169--560)}}} as {{{sqrt(169+560)}}}



{{{x = (-13 +- sqrt( 729 ))/(2(1))}}} Add {{{169}}} to {{{560}}} to get {{{729}}}



{{{x = (-13 +- sqrt( 729 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-13 +- 27)/(2)}}} Take the square root of {{{729}}} to get {{{27}}}. 



{{{x = (-13 + 27)/(2)}}} or {{{x = (-13 - 27)/(2)}}} Break up the expression. 



{{{x = (14)/(2)}}} or {{{x =  (-40)/(2)}}} Combine like terms. 



{{{x = 7}}} or {{{x = -20}}} Simplify. 



So the solutions are {{{x = 7}}} or {{{x = -20}}} 

  

Note: If you only need the positive solution, then just ignore {{{x = -20}}}