15r^2-7r-9=0

Solution for 15r^2-7r-9=0 equation:

Simplifying
15r2 + -7r + -9 = 0

Reorder the terms:
-9 + -7r + 15r2 = 0

Solving
-9 + -7r + 15r2 = 0

Solving for variable 'r'.

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

Divide each side by '15'.
-0.6 + -0.4666666667r + r2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -0.4666666667r + 0.6 + r2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -0.4666666667r + r2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -0.4666666667r + r2 = 0 + 0.6
-0.4666666667r + r2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-0.4666666667r + r2 = 0.6

The r term is -0.4666666667r.  Take half its coefficient (-0.2333333334).
Square it (0.05444444448) and add it to both sides.

Add '0.05444444448' to each side of the equation.
-0.4666666667r + 0.05444444448 + r2 = 0.6 + 0.05444444448

Reorder the terms:
0.05444444448 + -0.4666666667r + r2 = 0.6 + 0.05444444448

Combine like terms: 0.6 + 0.05444444448 = 0.65444444448
0.05444444448 + -0.4666666667r + r2 = 0.65444444448

Factor a perfect square on the left side:
(r + -0.2333333334)(r + -0.2333333334) = 0.65444444448

Calculate the square root of the right side: 0.808977407

Break this problem into two subproblems by setting 
(r + -0.2333333334) equal to 0.808977407 and -0.808977407.

Subproblem 1
r + -0.2333333334 = 0.808977407

Simplifying
r + -0.2333333334 = 0.808977407

Reorder the terms:
-0.2333333334 + r = 0.808977407

Solving
-0.2333333334 + r = 0.808977407

Solving for variable 'r'.

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

Add '0.2333333334' to each side of the equation.
-0.2333333334 + 0.2333333334 + r = 0.808977407 + 0.2333333334

Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000
0.0000000000 + r = 0.808977407 + 0.2333333334
r = 0.808977407 + 0.2333333334

Combine like terms: 0.808977407 + 0.2333333334 = 1.0423107404
r = 1.0423107404

Simplifying
r = 1.0423107404

Subproblem 2
r + -0.2333333334 = -0.808977407

Simplifying
r + -0.2333333334 = -0.808977407

Reorder the terms:
-0.2333333334 + r = -0.808977407

Solving
-0.2333333334 + r = -0.808977407

Solving for variable 'r'.

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

Add '0.2333333334' to each side of the equation.
-0.2333333334 + 0.2333333334 + r = -0.808977407 + 0.2333333334

Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000
0.0000000000 + r = -0.808977407 + 0.2333333334
r = -0.808977407 + 0.2333333334

Combine like terms: -0.808977407 + 0.2333333334 = -0.5756440736
r = -0.5756440736

Simplifying
r = -0.5756440736

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.0423107404, -0.5756440736}