25*(.75-x)=220*x(.75-x)+76.561*x

Solution for 25*(.75-x)=220*x(.75-x)+76.561*x equation:

Simplifying
25(0.75 + -1x) = 220x(0.75 + -1x) + 76.561x
(0.75 * 25 + -1x * 25) = 220x(0.75 + -1x) + 76.561x
(18.75 + -25x) = 220x(0.75 + -1x) + 76.561x
18.75 + -25x = (0.75 * 220x + -1x * 220x) + 76.561x
18.75 + -25x = (165x + -220x2) + 76.561x

Reorder the terms:
18.75 + -25x = 165x + 76.561x + -220x2

Combine like terms: 165x + 76.561x = 241.561x
18.75 + -25x = 241.561x + -220x2

Solving
18.75 + -25x = 241.561x + -220x2

Solving for variable 'x'.

Combine like terms: -25x + -241.561x = -266.561x
18.75 + -266.561x + 220x2 = 241.561x + -220x2 + -241.561x + 220x2

Reorder the terms:
18.75 + -266.561x + 220x2 = 241.561x + -241.561x + -220x2 + 220x2

Combine like terms: 241.561x + -241.561x = 0.000
18.75 + -266.561x + 220x2 = 0.000 + -220x2 + 220x2
18.75 + -266.561x + 220x2 = -220x2 + 220x2

Combine like terms: -220x2 + 220x2 = 0
18.75 + -266.561x + 220x2 = 0

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

Divide each side by '220'.
0.08522727273 + -1.211640909x + x2 = 0

Move the constant term to the right:

Add '-0.08522727273' to each side of the equation.
0.08522727273 + -1.211640909x + -0.08522727273 + x2 = 0 + -0.08522727273

Reorder the terms:
0.08522727273 + -0.08522727273 + -1.211640909x + x2 = 0 + -0.08522727273

Combine like terms: 0.08522727273 + -0.08522727273 = 0.00000000000
0.00000000000 + -1.211640909x + x2 = 0 + -0.08522727273
-1.211640909x + x2 = 0 + -0.08522727273

Combine like terms: 0 + -0.08522727273 = -0.08522727273
-1.211640909x + x2 = -0.08522727273

The x term is -1.211640909x.  Take half its coefficient (-0.6058204545).
Square it (0.3670184231) and add it to both sides.

Add '0.3670184231' to each side of the equation.
-1.211640909x + 0.3670184231 + x2 = -0.08522727273 + 0.3670184231

Reorder the terms:
0.3670184231 + -1.211640909x + x2 = -0.08522727273 + 0.3670184231

Combine like terms: -0.08522727273 + 0.3670184231 = 0.28179115037
0.3670184231 + -1.211640909x + x2 = 0.28179115037

Factor a perfect square on the left side:
(x + -0.6058204545)(x + -0.6058204545) = 0.28179115037

Calculate the square root of the right side: 0.530840042

Break this problem into two subproblems by setting 
(x + -0.6058204545) equal to 0.530840042 and -0.530840042.

Subproblem 1
x + -0.6058204545 = 0.530840042

Simplifying
x + -0.6058204545 = 0.530840042

Reorder the terms:
-0.6058204545 + x = 0.530840042

Solving
-0.6058204545 + x = 0.530840042

Solving for variable 'x'.

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

Add '0.6058204545' to each side of the equation.
-0.6058204545 + 0.6058204545 + x = 0.530840042 + 0.6058204545

Combine like terms: -0.6058204545 + 0.6058204545 = 0.0000000000
0.0000000000 + x = 0.530840042 + 0.6058204545
x = 0.530840042 + 0.6058204545

Combine like terms: 0.530840042 + 0.6058204545 = 1.1366604965
x = 1.1366604965

Simplifying
x = 1.1366604965

Subproblem 2
x + -0.6058204545 = -0.530840042

Simplifying
x + -0.6058204545 = -0.530840042

Reorder the terms:
-0.6058204545 + x = -0.530840042

Solving
-0.6058204545 + x = -0.530840042

Solving for variable 'x'.

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

Add '0.6058204545' to each side of the equation.
-0.6058204545 + 0.6058204545 + x = -0.530840042 + 0.6058204545

Combine like terms: -0.6058204545 + 0.6058204545 = 0.0000000000
0.0000000000 + x = -0.530840042 + 0.6058204545
x = -0.530840042 + 0.6058204545

Combine like terms: -0.530840042 + 0.6058204545 = 0.0749804125
x = 0.0749804125

Simplifying
x = 0.0749804125

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1366604965, 0.0749804125}