3r^2+3r-4=0

Solution for 3r^2+3r-4=0 equation:

Simplifying
3r2 + 3r + -4 = 0

Reorder the terms:
-4 + 3r + 3r2 = 0

Solving
-4 + 3r + 3r2 = 0

Solving for variable 'r'.

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

Divide each side by '3'.
-1.333333333 + r + r2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + r + 1.333333333 + r2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + r + r2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + r + r2 = 0 + 1.333333333
r + r2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
r + r2 = 1.333333333

The r term is r.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + r2 = 1.333333333 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + r2 = 1.333333333 + 0.25

Combine like terms: 1.333333333 + 0.25 = 1.583333333
1.25 + r2 = 1.583333333

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 1.583333333

Calculate the square root of the right side: 1.258305739

Break this problem into two subproblems by setting 
(r + 0.5) equal to 1.258305739 and -1.258305739.

Subproblem 1
r + 0.5 = 1.258305739

Simplifying
r + 0.5 = 1.258305739

Reorder the terms:
0.5 + r = 1.258305739

Solving
0.5 + r = 1.258305739

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = 1.258305739 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = 1.258305739 + -0.5
r = 1.258305739 + -0.5

Combine like terms: 1.258305739 + -0.5 = 0.758305739
r = 0.758305739

Simplifying
r = 0.758305739

Subproblem 2
r + 0.5 = -1.258305739

Simplifying
r + 0.5 = -1.258305739

Reorder the terms:
0.5 + r = -1.258305739

Solving
0.5 + r = -1.258305739

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = -1.258305739 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = -1.258305739 + -0.5
r = -1.258305739 + -0.5

Combine like terms: -1.258305739 + -0.5 = -1.758305739
r = -1.758305739

Simplifying
r = -1.758305739

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.758305739, -1.758305739}