2r^2+6r-3=0

Solution for 2r^2+6r-3=0 equation:

Simplifying
2r2 + 6r + -3 = 0

Reorder the terms:
-3 + 6r + 2r2 = 0

Solving
-3 + 6r + 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'.
-1.5 + 3r + r2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 3r + 1.5 + r2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 3r + r2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 3r + r2 = 0 + 1.5
3r + r2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
3r + r2 = 1.5

The r term is 3r.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3r + 2.25 + r2 = 1.5 + 2.25

Reorder the terms:
2.25 + 3r + r2 = 1.5 + 2.25

Combine like terms: 1.5 + 2.25 = 3.75
2.25 + 3r + r2 = 3.75

Factor a perfect square on the left side:
(r + 1.5)(r + 1.5) = 3.75

Calculate the square root of the right side: 1.936491673

Break this problem into two subproblems by setting 
(r + 1.5) equal to 1.936491673 and -1.936491673.

Subproblem 1
r + 1.5 = 1.936491673

Simplifying
r + 1.5 = 1.936491673

Reorder the terms:
1.5 + r = 1.936491673

Solving
1.5 + r = 1.936491673

Solving for variable 'r'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + r = 1.936491673 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + r = 1.936491673 + -1.5
r = 1.936491673 + -1.5

Combine like terms: 1.936491673 + -1.5 = 0.436491673
r = 0.436491673

Simplifying
r = 0.436491673

Subproblem 2
r + 1.5 = -1.936491673

Simplifying
r + 1.5 = -1.936491673

Reorder the terms:
1.5 + r = -1.936491673

Solving
1.5 + r = -1.936491673

Solving for variable 'r'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + r = -1.936491673 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + r = -1.936491673 + -1.5
r = -1.936491673 + -1.5

Combine like terms: -1.936491673 + -1.5 = -3.436491673
r = -3.436491673

Simplifying
r = -3.436491673

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.436491673, -3.436491673}