80r=705600r^2-6350400

Solution for 80r=705600r^2-6350400 equation:

Simplifying
80r = 705600r2 + -6350400

Reorder the terms:
80r = -6350400 + 705600r2

Solving
80r = -6350400 + 705600r2

Solving for variable 'r'.

Reorder the terms:
6350400 + 80r + -705600r2 = -6350400 + 705600r2 + 6350400 + -705600r2

Reorder the terms:
6350400 + 80r + -705600r2 = -6350400 + 6350400 + 705600r2 + -705600r2

Combine like terms: -6350400 + 6350400 = 0
6350400 + 80r + -705600r2 = 0 + 705600r2 + -705600r2
6350400 + 80r + -705600r2 = 705600r2 + -705600r2

Combine like terms: 705600r2 + -705600r2 = 0
6350400 + 80r + -705600r2 = 0

Factor out the Greatest Common Factor (GCF), '80'.
80(79380 + r + -8820r2) = 0

Ignore the factor 80.
Subproblem 1
Set the factor '(79380 + r + -8820r2)' equal to zero and attempt to solve:

Simplifying
79380 + r + -8820r2 = 0

Solving
79380 + r + -8820r2 = 0

Begin completing the square.  Divide all terms by
-8820 the coefficient of the squared term: 

Divide each side by '-8820'.
-9 + -0.0001133786848r + r2 = 0.0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -0.0001133786848r + 9 + r2 = 0.0 + 9

Reorder the terms:
-9 + 9 + -0.0001133786848r + r2 = 0.0 + 9

Combine like terms: -9 + 9 = 0
0 + -0.0001133786848r + r2 = 0.0 + 9
-0.0001133786848r + r2 = 0.0 + 9

Combine like terms: 0.0 + 9 = 9
-0.0001133786848r + r2 = 9

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.
-0.0001133786848r + 0.25 + r2 = 9 + 0.25

Reorder the terms:
0.25 + -0.0001133786848r + r2 = 9 + 0.25

Combine like terms: 9 + 0.25 = 9.25
0.25 + -0.0001133786848r + r2 = 9.25

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(r + 0.5) equal to 3.041381265 and -3.041381265.

Subproblem 1
r + 0.5 = 3.041381265

Simplifying
r + 0.5 = 3.041381265

Reorder the terms:
0.5 + r = 3.041381265

Solving
0.5 + r = 3.041381265

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 = 3.041381265 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = 3.041381265 + -0.5
r = 3.041381265 + -0.5

Combine like terms: 3.041381265 + -0.5 = 2.541381265
r = 2.541381265

Simplifying
r = 2.541381265

Subproblem 2
r + 0.5 = -3.041381265

Simplifying
r + 0.5 = -3.041381265

Reorder the terms:
0.5 + r = -3.041381265

Solving
0.5 + r = -3.041381265

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 = -3.041381265 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = -3.041381265 + -0.5
r = -3.041381265 + -0.5

Combine like terms: -3.041381265 + -0.5 = -3.541381265
r = -3.541381265

Simplifying
r = -3.541381265

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.541381265, -3.541381265}
Solution
r = {2.541381265, -3.541381265}