5x(x-4)-17=4(x-1)

Solution for 5x(x-4)-17=4(x-1) equation:

Simplifying
5x(x + -4) + -17 = 4(x + -1)

Reorder the terms:
5x(-4 + x) + -17 = 4(x + -1)
(-4 * 5x + x * 5x) + -17 = 4(x + -1)
(-20x + 5x2) + -17 = 4(x + -1)

Reorder the terms:
-17 + -20x + 5x2 = 4(x + -1)

Reorder the terms:
-17 + -20x + 5x2 = 4(-1 + x)
-17 + -20x + 5x2 = (-1 * 4 + x * 4)
-17 + -20x + 5x2 = (-4 + 4x)

Solving
-17 + -20x + 5x2 = -4 + 4x

Solving for variable 'x'.

Reorder the terms:
-17 + 4 + -20x + -4x + 5x2 = -4 + 4x + 4 + -4x

Combine like terms: -17 + 4 = -13
-13 + -20x + -4x + 5x2 = -4 + 4x + 4 + -4x

Combine like terms: -20x + -4x = -24x
-13 + -24x + 5x2 = -4 + 4x + 4 + -4x

Reorder the terms:
-13 + -24x + 5x2 = -4 + 4 + 4x + -4x

Combine like terms: -4 + 4 = 0
-13 + -24x + 5x2 = 0 + 4x + -4x
-13 + -24x + 5x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-13 + -24x + 5x2 = 0

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

Divide each side by '5'.
-2.6 + -4.8x + x2 = 0

Move the constant term to the right:

Add '2.6' to each side of the equation.
-2.6 + -4.8x + 2.6 + x2 = 0 + 2.6

Reorder the terms:
-2.6 + 2.6 + -4.8x + x2 = 0 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + -4.8x + x2 = 0 + 2.6
-4.8x + x2 = 0 + 2.6

Combine like terms: 0 + 2.6 = 2.6
-4.8x + x2 = 2.6

The x term is -4.8x.  Take half its coefficient (-2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
-4.8x + 5.76 + x2 = 2.6 + 5.76

Reorder the terms:
5.76 + -4.8x + x2 = 2.6 + 5.76

Combine like terms: 2.6 + 5.76 = 8.36
5.76 + -4.8x + x2 = 8.36

Factor a perfect square on the left side:
(x + -2.4)(x + -2.4) = 8.36

Calculate the square root of the right side: 2.891366459

Break this problem into two subproblems by setting 
(x + -2.4) equal to 2.891366459 and -2.891366459.

Subproblem 1
x + -2.4 = 2.891366459

Simplifying
x + -2.4 = 2.891366459

Reorder the terms:
-2.4 + x = 2.891366459

Solving
-2.4 + x = 2.891366459

Solving for variable 'x'.

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

Add '2.4' to each side of the equation.
-2.4 + 2.4 + x = 2.891366459 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + x = 2.891366459 + 2.4
x = 2.891366459 + 2.4

Combine like terms: 2.891366459 + 2.4 = 5.291366459
x = 5.291366459

Simplifying
x = 5.291366459

Subproblem 2
x + -2.4 = -2.891366459

Simplifying
x + -2.4 = -2.891366459

Reorder the terms:
-2.4 + x = -2.891366459

Solving
-2.4 + x = -2.891366459

Solving for variable 'x'.

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

Add '2.4' to each side of the equation.
-2.4 + 2.4 + x = -2.891366459 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + x = -2.891366459 + 2.4
x = -2.891366459 + 2.4

Combine like terms: -2.891366459 + 2.4 = -0.491366459
x = -0.491366459

Simplifying
x = -0.491366459

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.291366459, -0.491366459}