Get the constant term +29 off the left side:




Divide through by the leading coefficient 4





To the side, multiply the coefficient of p, which is -8
by 1/2, getting -4, then square -4, getting (-4)² = 16.
Then add +16 to both sides:



This causes the left side to became a trinomial which
when factored becomes a perfect square.  And we get an
LCD on the right of 4 




Write the left side as a perfect square.  Combine
the fractions on the right:



Use the principle of square roots:



We can take the square root of 4 on the bottom
on the right:



Solve for p by adding 4 to both sides:



You can leave it like that or you can
get an LCD of 2



And then combine the two fractions



The two solutions are:

 and 

Edwin