4p^2+24p-5=0

Solution for 4p^2+24p-5=0 equation:

Simplifying
4p2 + 24p + -5 = 0

Reorder the terms:
-5 + 24p + 4p2 = 0

Solving
-5 + 24p + 4p2 = 0

Solving for variable 'p'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-1.25 + 6p + p2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 6p + 1.25 + p2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 6p + p2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 6p + p2 = 0 + 1.25
6p + p2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
6p + p2 = 1.25

The p term is 6p.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6p + 9 + p2 = 1.25 + 9

Reorder the terms:
9 + 6p + p2 = 1.25 + 9

Combine like terms: 1.25 + 9 = 10.25
9 + 6p + p2 = 10.25

Factor a perfect square on the left side:
(p + 3)(p + 3) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(p + 3) equal to 3.201562119 and -3.201562119.

Subproblem 1
p + 3 = 3.201562119

Simplifying
p + 3 = 3.201562119

Reorder the terms:
3 + p = 3.201562119

Solving
3 + p = 3.201562119

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + p = 3.201562119 + -3

Combine like terms: 3 + -3 = 0
0 + p = 3.201562119 + -3
p = 3.201562119 + -3

Combine like terms: 3.201562119 + -3 = 0.201562119
p = 0.201562119

Simplifying
p = 0.201562119

Subproblem 2
p + 3 = -3.201562119

Simplifying
p + 3 = -3.201562119

Reorder the terms:
3 + p = -3.201562119

Solving
3 + p = -3.201562119

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + p = -3.201562119 + -3

Combine like terms: 3 + -3 = 0
0 + p = -3.201562119 + -3
p = -3.201562119 + -3

Combine like terms: -3.201562119 + -3 = -6.201562119
p = -6.201562119

Simplifying
p = -6.201562119

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.201562119, -6.201562119}