Question 566230

{{{4p^2-90=-9p}}} Start with the given equation.



{{{4p^2-90+9p=0}}} Get every term to the left side.



{{{4p^2+9p-90=0}}} Rearrange the terms.



Notice that the quadratic {{{4p^2+9p-90}}} is in the form of {{{Ap^2+Bp+C}}} where {{{A=4}}}, {{{B=9}}}, and {{{C=-90}}}



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



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



{{{p = (-(9) +- sqrt( (9)^2-4(4)(-90) ))/(2(4))}}} Plug in  {{{A=4}}}, {{{B=9}}}, and {{{C=-90}}}



{{{p = (-9 +- sqrt( 81-4(4)(-90) ))/(2(4))}}} Square {{{9}}} to get {{{81}}}. 



{{{p = (-9 +- sqrt( 81--1440 ))/(2(4))}}} Multiply {{{4(4)(-90)}}} to get {{{-1440}}}



{{{p = (-9 +- sqrt( 81+1440 ))/(2(4))}}} Rewrite {{{sqrt(81--1440)}}} as {{{sqrt(81+1440)}}}



{{{p = (-9 +- sqrt( 1521 ))/(2(4))}}} Add {{{81}}} to {{{1440}}} to get {{{1521}}}



{{{p = (-9 +- sqrt( 1521 ))/(8)}}} Multiply {{{2}}} and {{{4}}} to get {{{8}}}. 



{{{p = (-9 +- 39)/(8)}}} Take the square root of {{{1521}}} to get {{{39}}}. 



{{{p = (-9 + 39)/(8)}}} or {{{p = (-9 - 39)/(8)}}} Break up the expression. 



{{{p = (30)/(8)}}} or {{{p =  (-48)/(8)}}} Combine like terms. 



{{{p = 15/4}}} or {{{p = -6}}} Simplify. 



So the solutions are {{{p = 15/4}}} or {{{p = -6}}}