5p^2-13p-30=0

Solution for 5p^2-13p-30=0 equation:

Simplifying
5p2 + -13p + -30 = 0

Reorder the terms:
-30 + -13p + 5p2 = 0

Solving
-30 + -13p + 5p2 = 0

Solving for variable 'p'.

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

Divide each side by '5'.
-6 + -2.6p + p2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -2.6p + 6 + p2 = 0 + 6

Reorder the terms:
-6 + 6 + -2.6p + p2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -2.6p + p2 = 0 + 6
-2.6p + p2 = 0 + 6

Combine like terms: 0 + 6 = 6
-2.6p + p2 = 6

The p term is -2.6p.  Take half its coefficient (-1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
-2.6p + 1.69 + p2 = 6 + 1.69

Reorder the terms:
1.69 + -2.6p + p2 = 6 + 1.69

Combine like terms: 6 + 1.69 = 7.69
1.69 + -2.6p + p2 = 7.69

Factor a perfect square on the left side:
(p + -1.3)(p + -1.3) = 7.69

Calculate the square root of the right side: 2.773084925

Break this problem into two subproblems by setting 
(p + -1.3) equal to 2.773084925 and -2.773084925.

Subproblem 1
p + -1.3 = 2.773084925

Simplifying
p + -1.3 = 2.773084925

Reorder the terms:
-1.3 + p = 2.773084925

Solving
-1.3 + p = 2.773084925

Solving for variable 'p'.

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

Add '1.3' to each side of the equation.
-1.3 + 1.3 + p = 2.773084925 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + p = 2.773084925 + 1.3
p = 2.773084925 + 1.3

Combine like terms: 2.773084925 + 1.3 = 4.073084925
p = 4.073084925

Simplifying
p = 4.073084925

Subproblem 2
p + -1.3 = -2.773084925

Simplifying
p + -1.3 = -2.773084925

Reorder the terms:
-1.3 + p = -2.773084925

Solving
-1.3 + p = -2.773084925

Solving for variable 'p'.

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

Add '1.3' to each side of the equation.
-1.3 + 1.3 + p = -2.773084925 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + p = -2.773084925 + 1.3
p = -2.773084925 + 1.3

Combine like terms: -2.773084925 + 1.3 = -1.473084925
p = -1.473084925

Simplifying
p = -1.473084925

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {4.073084925, -1.473084925}