8x^2=16x-3

Solution for 8x^2=16x-3 equation:

Simplifying
8x2 = 16x + -3

Reorder the terms:
8x2 = -3 + 16x

Solving
8x2 = -3 + 16x

Solving for variable 'x'.

Reorder the terms:
3 + -16x + 8x2 = -3 + 16x + 3 + -16x

Reorder the terms:
3 + -16x + 8x2 = -3 + 3 + 16x + -16x

Combine like terms: -3 + 3 = 0
3 + -16x + 8x2 = 0 + 16x + -16x
3 + -16x + 8x2 = 16x + -16x

Combine like terms: 16x + -16x = 0
3 + -16x + 8x2 = 0

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

Divide each side by '8'.
0.375 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + -2x + -0.375 + x2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + -2x + x2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + -2x + x2 = 0 + -0.375
-2x + x2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
-2x + x2 = -0.375

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.375 + 1

Reorder the terms:
1 + -2x + x2 = -0.375 + 1

Combine like terms: -0.375 + 1 = 0.625
1 + -2x + x2 = 0.625

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.625

Calculate the square root of the right side: 0.790569415

Break this problem into two subproblems by setting 
(x + -1) equal to 0.790569415 and -0.790569415.

Subproblem 1
x + -1 = 0.790569415

Simplifying
x + -1 = 0.790569415

Reorder the terms:
-1 + x = 0.790569415

Solving
-1 + x = 0.790569415

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 0.790569415 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.790569415 + 1
x = 0.790569415 + 1

Combine like terms: 0.790569415 + 1 = 1.790569415
x = 1.790569415

Simplifying
x = 1.790569415

Subproblem 2
x + -1 = -0.790569415

Simplifying
x + -1 = -0.790569415

Reorder the terms:
-1 + x = -0.790569415

Solving
-1 + x = -0.790569415

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -0.790569415 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.790569415 + 1
x = -0.790569415 + 1

Combine like terms: -0.790569415 + 1 = 0.209430585
x = 0.209430585

Simplifying
x = 0.209430585

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.790569415, 0.209430585}