0=0.25*((0.851*(15-1.75*x)-2.5)*(0.85*(15-1.75*x)-2.5))

Solution for 0=0.25*((0.851*(15-1.75*x)-2.5)*(0.85*(15-1.75*x)-2.5)) equation:

Simplifying
0 = 0.25((0.851(15 + -1.75x) + -2.5)(0.85(15 + -1.75x) + -2.5))
0 = 0.25(((15 * 0.851 + -1.75x * 0.851) + -2.5)(0.85(15 + -1.75x) + -2.5))
0 = 0.25(((12.765 + -1.48925x) + -2.5)(0.85(15 + -1.75x) + -2.5))

Reorder the terms:
0 = 0.25((12.765 + -2.5 + -1.48925x)(0.85(15 + -1.75x) + -2.5))

Combine like terms: 12.765 + -2.5 = 10.265
0 = 0.25((10.265 + -1.48925x)(0.85(15 + -1.75x) + -2.5))
0 = 0.25((10.265 + -1.48925x)((15 * 0.85 + -1.75x * 0.85) + -2.5))
0 = 0.25((10.265 + -1.48925x)((12.75 + -1.4875x) + -2.5))

Reorder the terms:
0 = 0.25((10.265 + -1.48925x)(12.75 + -2.5 + -1.4875x))

Combine like terms: 12.75 + -2.5 = 10.25
0 = 0.25((10.265 + -1.48925x)(10.25 + -1.4875x))

Multiply (10.265 + -1.48925x) * (10.25 + -1.4875x)
0 = 0.25((10.265(10.25 + -1.4875x) + -1.48925x * (10.25 + -1.4875x)))
0 = 0.25(((10.25 * 10.265 + -1.4875x * 10.265) + -1.48925x * (10.25 + -1.4875x)))
0 = 0.25(((105.21625 + -15.2691875x) + -1.48925x * (10.25 + -1.4875x)))
0 = 0.25((105.21625 + -15.2691875x + (10.25 * -1.48925x + -1.4875x * -1.48925x)))
0 = 0.25((105.21625 + -15.2691875x + (-15.2648125x + 2.215259375x2)))

Combine like terms: -15.2691875x + -15.2648125x = -30.534x
0 = 0.25((105.21625 + -30.534x + 2.215259375x2))
0 = (105.21625 * 0.25 + -30.534x * 0.25 + 2.215259375x2 * 0.25)
0 = (26.3040625 + -7.6335x + 0.5538148438x2)

Solving
0 = 26.3040625 + -7.6335x + 0.5538148438x2

Solving for variable 'x'.

Combine like terms: 0 + -26.3040625 = -26.3040625
-26.3040625 + 7.6335x + -0.5538148438x2 = 26.3040625 + -7.6335x + 0.5538148438x2 + -26.3040625 + 7.6335x + -0.5538148438x2

Reorder the terms:
-26.3040625 + 7.6335x + -0.5538148438x2 = 26.3040625 + -26.3040625 + -7.6335x + 7.6335x + 0.5538148438x2 + -0.5538148438x2

Combine like terms: 26.3040625 + -26.3040625 = 0.0000000
-26.3040625 + 7.6335x + -0.5538148438x2 = 0.0000000 + -7.6335x + 7.6335x + 0.5538148438x2 + -0.5538148438x2
-26.3040625 + 7.6335x + -0.5538148438x2 = -7.6335x + 7.6335x + 0.5538148438x2 + -0.5538148438x2

Combine like terms: -7.6335x + 7.6335x = 0.0000
-26.3040625 + 7.6335x + -0.5538148438x2 = 0.0000 + 0.5538148438x2 + -0.5538148438x2
-26.3040625 + 7.6335x + -0.5538148438x2 = 0.5538148438x2 + -0.5538148438x2

Combine like terms: 0.5538148438x2 + -0.5538148438x2 = 0.0000000000
-26.3040625 + 7.6335x + -0.5538148438x2 = 0.0000000000

Begin completing the square.  Divide all terms by
-0.5538148438 the coefficient of the squared term: 

Divide each side by '-0.5538148438'.
47.49613123 + -13.78348754x + x2 = 0

Move the constant term to the right:

Add '-47.49613123' to each side of the equation.
47.49613123 + -13.78348754x + -47.49613123 + x2 = 0 + -47.49613123

Reorder the terms:
47.49613123 + -47.49613123 + -13.78348754x + x2 = 0 + -47.49613123

Combine like terms: 47.49613123 + -47.49613123 = 0.00000000
0.00000000 + -13.78348754x + x2 = 0 + -47.49613123
-13.78348754x + x2 = 0 + -47.49613123

Combine like terms: 0 + -47.49613123 = -47.49613123
-13.78348754x + x2 = -47.49613123

The x term is -13.78348754x.  Take half its coefficient (-6.89174377).
Square it (47.49613219) and add it to both sides.

Add '47.49613219' to each side of the equation.
-13.78348754x + 47.49613219 + x2 = -47.49613123 + 47.49613219

Reorder the terms:
47.49613219 + -13.78348754x + x2 = -47.49613123 + 47.49613219

Combine like terms: -47.49613123 + 47.49613219 = 0.00000096
47.49613219 + -13.78348754x + x2 = 0.00000096

Factor a perfect square on the left side:
(x + -6.89174377)(x + -6.89174377) = 0.00000096

Calculate the square root of the right side: 0.000979796

Break this problem into two subproblems by setting 
(x + -6.89174377) equal to 0.000979796 and -0.000979796.

Subproblem 1
x + -6.89174377 = 0.000979796

Simplifying
x + -6.89174377 = 0.000979796

Reorder the terms:
-6.89174377 + x = 0.000979796

Solving
-6.89174377 + x = 0.000979796

Solving for variable 'x'.

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

Add '6.89174377' to each side of the equation.
-6.89174377 + 6.89174377 + x = 0.000979796 + 6.89174377

Combine like terms: -6.89174377 + 6.89174377 = 0.00000000
0.00000000 + x = 0.000979796 + 6.89174377
x = 0.000979796 + 6.89174377

Combine like terms: 0.000979796 + 6.89174377 = 6.892723566
x = 6.892723566

Simplifying
x = 6.892723566

Subproblem 2
x + -6.89174377 = -0.000979796

Simplifying
x + -6.89174377 = -0.000979796

Reorder the terms:
-6.89174377 + x = -0.000979796

Solving
-6.89174377 + x = -0.000979796

Solving for variable 'x'.

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

Add '6.89174377' to each side of the equation.
-6.89174377 + 6.89174377 + x = -0.000979796 + 6.89174377

Combine like terms: -6.89174377 + 6.89174377 = 0.00000000
0.00000000 + x = -0.000979796 + 6.89174377
x = -0.000979796 + 6.89174377

Combine like terms: -0.000979796 + 6.89174377 = 6.890763974
x = 6.890763974

Simplifying
x = 6.890763974

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.892723566, 6.890763974}