2w^2-5w+6=8

Solution for 2w^2-5w+6=8 equation:

Simplifying
2w2 + -5w + 6 = 8

Reorder the terms:
6 + -5w + 2w2 = 8

Solving
6 + -5w + 2w2 = 8

Solving for variable 'w'.

Reorder the terms:
6 + -8 + -5w + 2w2 = 8 + -8

Combine like terms: 6 + -8 = -2
-2 + -5w + 2w2 = 8 + -8

Combine like terms: 8 + -8 = 0
-2 + -5w + 2w2 = 0

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

Divide each side by '2'.
-1 + -2.5w + w2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2.5w + 1 + w2 = 0 + 1

Reorder the terms:
-1 + 1 + -2.5w + w2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2.5w + w2 = 0 + 1
-2.5w + w2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2.5w + w2 = 1

The w term is -2.5w.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5w + 1.5625 + w2 = 1 + 1.5625

Reorder the terms:
1.5625 + -2.5w + w2 = 1 + 1.5625

Combine like terms: 1 + 1.5625 = 2.5625
1.5625 + -2.5w + w2 = 2.5625

Factor a perfect square on the left side:
(w + -1.25)(w + -1.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(w + -1.25) equal to 1.600781059 and -1.600781059.

Subproblem 1
w + -1.25 = 1.600781059

Simplifying
w + -1.25 = 1.600781059

Reorder the terms:
-1.25 + w = 1.600781059

Solving
-1.25 + w = 1.600781059

Solving for variable 'w'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + w = 1.600781059 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + w = 1.600781059 + 1.25
w = 1.600781059 + 1.25

Combine like terms: 1.600781059 + 1.25 = 2.850781059
w = 2.850781059

Simplifying
w = 2.850781059

Subproblem 2
w + -1.25 = -1.600781059

Simplifying
w + -1.25 = -1.600781059

Reorder the terms:
-1.25 + w = -1.600781059

Solving
-1.25 + w = -1.600781059

Solving for variable 'w'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + w = -1.600781059 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + w = -1.600781059 + 1.25
w = -1.600781059 + 1.25

Combine like terms: -1.600781059 + 1.25 = -0.350781059
w = -0.350781059

Simplifying
w = -0.350781059

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.850781059, -0.350781059}