4w^2=10w-8

Solution for 4w^2=10w-8 equation:

Simplifying
4w2 = 10w + -8

Reorder the terms:
4w2 = -8 + 10w

Solving
4w2 = -8 + 10w

Solving for variable 'w'.

Reorder the terms:
8 + -10w + 4w2 = -8 + 10w + 8 + -10w

Reorder the terms:
8 + -10w + 4w2 = -8 + 8 + 10w + -10w

Combine like terms: -8 + 8 = 0
8 + -10w + 4w2 = 0 + 10w + -10w
8 + -10w + 4w2 = 10w + -10w

Combine like terms: 10w + -10w = 0
8 + -10w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -5w + 2w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -5w + 2w2)' equal to zero and attempt to solve:

Simplifying
4 + -5w + 2w2 = 0

Solving
4 + -5w + 2w2 = 0

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

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

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -2.5w + -2 + w2 = 0 + -2

Reorder the terms:
2 + -2 + -2.5w + w2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -2.5w + w2 = 0 + -2
-2.5w + w2 = 0 + -2

Combine like terms: 0 + -2 = -2
-2.5w + w2 = -2

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 = -2 + 1.5625

Reorder the terms:
1.5625 + -2.5w + w2 = -2 + 1.5625

Combine like terms: -2 + 1.5625 = -0.4375
1.5625 + -2.5w + w2 = -0.4375

Factor a perfect square on the left side:
(w + -1.25)(w + -1.25) = -0.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.