8=x*(78-2*(x-1))

Solution for 8=x*(78-2*(x-1)) equation:

Simplifying
8 = x(78 + -2(x + -1))

Reorder the terms:
8 = x(78 + -2(-1 + x))
8 = x(78 + (-1 * -2 + x * -2))
8 = x(78 + (2 + -2x))

Combine like terms: 78 + 2 = 80
8 = x(80 + -2x)
8 = (80 * x + -2x * x)
8 = (80x + -2x2)

Solving
8 = 80x + -2x2

Solving for variable 'x'.

Reorder the terms:
8 + -80x + 2x2 = 80x + -80x + -2x2 + 2x2

Combine like terms: 80x + -80x = 0
8 + -80x + 2x2 = 0 + -2x2 + 2x2
8 + -80x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
8 + -80x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -40x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -40x + x2)' equal to zero and attempt to solve:

Simplifying
4 + -40x + x2 = 0

Solving
4 + -40x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -40x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -40x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -40x + x2 = 0 + -4
-40x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-40x + x2 = -4

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = -4 + 400

Reorder the terms:
400 + -40x + x2 = -4 + 400

Combine like terms: -4 + 400 = 396
400 + -40x + x2 = 396

Factor a perfect square on the left side:
(x + -20)(x + -20) = 396

Calculate the square root of the right side: 19.899748742

Break this problem into two subproblems by setting 
(x + -20) equal to 19.899748742 and -19.899748742.

Subproblem 1
x + -20 = 19.899748742

Simplifying
x + -20 = 19.899748742

Reorder the terms:
-20 + x = 19.899748742

Solving
-20 + x = 19.899748742

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = 19.899748742 + 20

Combine like terms: -20 + 20 = 0
0 + x = 19.899748742 + 20
x = 19.899748742 + 20

Combine like terms: 19.899748742 + 20 = 39.899748742
x = 39.899748742

Simplifying
x = 39.899748742

Subproblem 2
x + -20 = -19.899748742

Simplifying
x + -20 = -19.899748742

Reorder the terms:
-20 + x = -19.899748742

Solving
-20 + x = -19.899748742

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = -19.899748742 + 20

Combine like terms: -20 + 20 = 0
0 + x = -19.899748742 + 20
x = -19.899748742 + 20

Combine like terms: -19.899748742 + 20 = 0.100251258
x = 0.100251258

Simplifying
x = 0.100251258

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {39.899748742, 0.100251258}
Solution
x = {39.899748742, 0.100251258}