3r^2-146r+720=0

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Solution for 3r^2-146r+720=0 equation:


Simplifying
3r2 + -146r + 720 = 0

Reorder the terms:
720 + -146r + 3r2 = 0

Solving
720 + -146r + 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'.
240 + -48.66666667r + r2 = 0

Move the constant term to the right:

Add '-240' to each side of the equation.
240 + -48.66666667r + -240 + r2 = 0 + -240

Reorder the terms:
240 + -240 + -48.66666667r + r2 = 0 + -240

Combine like terms: 240 + -240 = 0
0 + -48.66666667r + r2 = 0 + -240
-48.66666667r + r2 = 0 + -240

Combine like terms: 0 + -240 = -240
-48.66666667r + r2 = -240

The r term is -48.66666667r.  Take half its coefficient (-24.33333334).
Square it (592.1111114) and add it to both sides.

Add '592.1111114' to each side of the equation.
-48.66666667r + 592.1111114 + r2 = -240 + 592.1111114

Reorder the terms:
592.1111114 + -48.66666667r + r2 = -240 + 592.1111114

Combine like terms: -240 + 592.1111114 = 352.1111114
592.1111114 + -48.66666667r + r2 = 352.1111114

Factor a perfect square on the left side:
(r + -24.33333334)(r + -24.33333334) = 352.1111114

Calculate the square root of the right side: 18.764623934

Break this problem into two subproblems by setting 
(r + -24.33333334) equal to 18.764623934 and -18.764623934.


Subproblem 1
r + -24.33333334 = 18.764623934

Simplifying
r + -24.33333334 = 18.764623934

Reorder the terms:
-24.33333334 + r = 18.764623934

Solving
-24.33333334 + r = 18.764623934

Solving for variable 'r'.

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

Add '24.33333334' to each side of the equation.
-24.33333334 + 24.33333334 + r = 18.764623934 + 24.33333334

Combine like terms: -24.33333334 + 24.33333334 = 0.00000000
0.00000000 + r = 18.764623934 + 24.33333334
r = 18.764623934 + 24.33333334

Combine like terms: 18.764623934 + 24.33333334 = 43.097957274
r = 43.097957274

Simplifying
r = 43.097957274


Subproblem 2
r + -24.33333334 = -18.764623934

Simplifying
r + -24.33333334 = -18.764623934

Reorder the terms:
-24.33333334 + r = -18.764623934

Solving
-24.33333334 + r = -18.764623934

Solving for variable 'r'.

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

Add '24.33333334' to each side of the equation.
-24.33333334 + 24.33333334 + r = -18.764623934 + 24.33333334

Combine like terms: -24.33333334 + 24.33333334 = 0.00000000
0.00000000 + r = -18.764623934 + 24.33333334
r = -18.764623934 + 24.33333334

Combine like terms: -18.764623934 + 24.33333334 = 5.568709406
r = 5.568709406

Simplifying
r = 5.568709406


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {43.097957274, 5.568709406}

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