2r^2+13r-5=0

Solution for 2r^2+13r-5=0 equation:

Simplifying
2r2 + 13r + -5 = 0

Reorder the terms:
-5 + 13r + 2r2 = 0

Solving
-5 + 13r + 2r2 = 0

Solving for variable 'r'.

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

Divide each side by '2'.
-2.5 + 6.5r + r2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 6.5r + 2.5 + r2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 6.5r + r2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 6.5r + r2 = 0 + 2.5
6.5r + r2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
6.5r + r2 = 2.5

The r term is 6.5r.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5r + 10.5625 + r2 = 2.5 + 10.5625

Reorder the terms:
10.5625 + 6.5r + r2 = 2.5 + 10.5625

Combine like terms: 2.5 + 10.5625 = 13.0625
10.5625 + 6.5r + r2 = 13.0625

Factor a perfect square on the left side:
(r + 3.25)(r + 3.25) = 13.0625

Calculate the square root of the right side: 3.614208074

Break this problem into two subproblems by setting 
(r + 3.25) equal to 3.614208074 and -3.614208074.

Subproblem 1
r + 3.25 = 3.614208074

Simplifying
r + 3.25 = 3.614208074

Reorder the terms:
3.25 + r = 3.614208074

Solving
3.25 + r = 3.614208074

Solving for variable 'r'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + r = 3.614208074 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + r = 3.614208074 + -3.25
r = 3.614208074 + -3.25

Combine like terms: 3.614208074 + -3.25 = 0.364208074
r = 0.364208074

Simplifying
r = 0.364208074

Subproblem 2
r + 3.25 = -3.614208074

Simplifying
r + 3.25 = -3.614208074

Reorder the terms:
3.25 + r = -3.614208074

Solving
3.25 + r = -3.614208074

Solving for variable 'r'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + r = -3.614208074 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + r = -3.614208074 + -3.25
r = -3.614208074 + -3.25

Combine like terms: -3.614208074 + -3.25 = -6.864208074
r = -6.864208074

Simplifying
r = -6.864208074

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.364208074, -6.864208074}