-4w^2+20w-3=0

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Solution for -4w^2+20w-3=0 equation: 


Simplifying
-4w2 + 20w + -3 = 0

Reorder the terms:
-3 + 20w + -4w2 = 0

Solving
-3 + 20w + -4w2 = 0

Solving for variable 'w'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
0.75 + -5w + w2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -5w + -0.75 + w2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -5w + w2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -5w + w2 = 0 + -0.75
-5w + w2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-5w + w2 = -0.75

The w term is -5w.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5w + 6.25 + w2 = -0.75 + 6.25

Reorder the terms:
6.25 + -5w + w2 = -0.75 + 6.25

Combine like terms: -0.75 + 6.25 = 5.5
6.25 + -5w + w2 = 5.5

Factor a perfect square on the left side:
(w + -2.5)(w + -2.5) = 5.5

Calculate the square root of the right side: 2.34520788

Break this problem into two subproblems by setting 
(w + -2.5) equal to 2.34520788 and -2.34520788.


Subproblem 1
w + -2.5 = 2.34520788

Simplifying
w + -2.5 = 2.34520788

Reorder the terms:
-2.5 + w = 2.34520788

Solving
-2.5 + w = 2.34520788

Solving for variable 'w'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + w = 2.34520788 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + w = 2.34520788 + 2.5
w = 2.34520788 + 2.5

Combine like terms: 2.34520788 + 2.5 = 4.84520788
w = 4.84520788

Simplifying
w = 4.84520788


Subproblem 2
w + -2.5 = -2.34520788

Simplifying
w + -2.5 = -2.34520788

Reorder the terms:
-2.5 + w = -2.34520788

Solving
-2.5 + w = -2.34520788

Solving for variable 'w'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + w = -2.34520788 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + w = -2.34520788 + 2.5
w = -2.34520788 + 2.5

Combine like terms: -2.34520788 + 2.5 = 0.15479212
w = 0.15479212

Simplifying
w = 0.15479212


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.84520788, 0.15479212}

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