x^2+60x+2000=180x-0.4x^2

Solution for x^2+60x+2000=180x-0.4x^2 equation:

Simplifying
x2 + 60x + 2000 = 180x + -0.4x2

Reorder the terms:
2000 + 60x + x2 = 180x + -0.4x2

Solving
2000 + 60x + x2 = 180x + -0.4x2

Solving for variable 'x'.

Reorder the terms:
2000 + 60x + -180x + x2 + 0.4x2 = 180x + -0.4x2 + -180x + 0.4x2

Combine like terms: 60x + -180x = -120x
2000 + -120x + x2 + 0.4x2 = 180x + -0.4x2 + -180x + 0.4x2

Combine like terms: x2 + 0.4x2 = 1.4x2
2000 + -120x + 1.4x2 = 180x + -0.4x2 + -180x + 0.4x2

Reorder the terms:
2000 + -120x + 1.4x2 = 180x + -180x + -0.4x2 + 0.4x2

Combine like terms: 180x + -180x = 0
2000 + -120x + 1.4x2 = 0 + -0.4x2 + 0.4x2
2000 + -120x + 1.4x2 = -0.4x2 + 0.4x2

Combine like terms: -0.4x2 + 0.4x2 = 0.0
2000 + -120x + 1.4x2 = 0.0

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

Divide each side by '1.4'.
1428.571429 + -85.71428571x + x2 = 0

Move the constant term to the right:

Add '-1428.571429' to each side of the equation.
1428.571429 + -85.71428571x + -1428.571429 + x2 = 0 + -1428.571429

Reorder the terms:
1428.571429 + -1428.571429 + -85.71428571x + x2 = 0 + -1428.571429

Combine like terms: 1428.571429 + -1428.571429 = 0.000000
0.000000 + -85.71428571x + x2 = 0 + -1428.571429
-85.71428571x + x2 = 0 + -1428.571429

Combine like terms: 0 + -1428.571429 = -1428.571429
-85.71428571x + x2 = -1428.571429

The x term is -85.71428571x.  Take half its coefficient (-42.85714286).
Square it (1836.734694) and add it to both sides.

Add '1836.734694' to each side of the equation.
-85.71428571x + 1836.734694 + x2 = -1428.571429 + 1836.734694

Reorder the terms:
1836.734694 + -85.71428571x + x2 = -1428.571429 + 1836.734694

Combine like terms: -1428.571429 + 1836.734694 = 408.163265
1836.734694 + -85.71428571x + x2 = 408.163265

Factor a perfect square on the left side:
(x + -42.85714286)(x + -42.85714286) = 408.163265

Calculate the square root of the right side: 20.203050883

Break this problem into two subproblems by setting 
(x + -42.85714286) equal to 20.203050883 and -20.203050883.

Subproblem 1
x + -42.85714286 = 20.203050883

Simplifying
x + -42.85714286 = 20.203050883

Reorder the terms:
-42.85714286 + x = 20.203050883

Solving
-42.85714286 + x = 20.203050883

Solving for variable 'x'.

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

Add '42.85714286' to each side of the equation.
-42.85714286 + 42.85714286 + x = 20.203050883 + 42.85714286

Combine like terms: -42.85714286 + 42.85714286 = 0.00000000
0.00000000 + x = 20.203050883 + 42.85714286
x = 20.203050883 + 42.85714286

Combine like terms: 20.203050883 + 42.85714286 = 63.060193743
x = 63.060193743

Simplifying
x = 63.060193743

Subproblem 2
x + -42.85714286 = -20.203050883

Simplifying
x + -42.85714286 = -20.203050883

Reorder the terms:
-42.85714286 + x = -20.203050883

Solving
-42.85714286 + x = -20.203050883

Solving for variable 'x'.

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

Add '42.85714286' to each side of the equation.
-42.85714286 + 42.85714286 + x = -20.203050883 + 42.85714286

Combine like terms: -42.85714286 + 42.85714286 = 0.00000000
0.00000000 + x = -20.203050883 + 42.85714286
x = -20.203050883 + 42.85714286

Combine like terms: -20.203050883 + 42.85714286 = 22.654091977
x = 22.654091977

Simplifying
x = 22.654091977

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {63.060193743, 22.654091977}