-3w^2-20w+45=0

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Solution for -3w^2-20w+45=0 equation: 


Simplifying
-3w2 + -20w + 45 = 0

Reorder the terms:
45 + -20w + -3w2 = 0

Solving
45 + -20w + -3w2 = 0

Solving for variable 'w'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-15 + 6.666666667w + w2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 6.666666667w + 15 + w2 = 0 + 15

Reorder the terms:
-15 + 15 + 6.666666667w + w2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 6.666666667w + w2 = 0 + 15
6.666666667w + w2 = 0 + 15

Combine like terms: 0 + 15 = 15
6.666666667w + w2 = 15

The w term is 6.666666667w.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667w + 11.11111112 + w2 = 15 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667w + w2 = 15 + 11.11111112

Combine like terms: 15 + 11.11111112 = 26.11111112
11.11111112 + 6.666666667w + w2 = 26.11111112

Factor a perfect square on the left side:
(w + 3.333333334)(w + 3.333333334) = 26.11111112

Calculate the square root of the right side: 5.10990324

Break this problem into two subproblems by setting 
(w + 3.333333334) equal to 5.10990324 and -5.10990324.


Subproblem 1
w + 3.333333334 = 5.10990324

Simplifying
w + 3.333333334 = 5.10990324

Reorder the terms:
3.333333334 + w = 5.10990324

Solving
3.333333334 + w = 5.10990324

Solving for variable 'w'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + w = 5.10990324 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + w = 5.10990324 + -3.333333334
w = 5.10990324 + -3.333333334

Combine like terms: 5.10990324 + -3.333333334 = 1.776569906
w = 1.776569906

Simplifying
w = 1.776569906


Subproblem 2
w + 3.333333334 = -5.10990324

Simplifying
w + 3.333333334 = -5.10990324

Reorder the terms:
3.333333334 + w = -5.10990324

Solving
3.333333334 + w = -5.10990324

Solving for variable 'w'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + w = -5.10990324 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + w = -5.10990324 + -3.333333334
w = -5.10990324 + -3.333333334

Combine like terms: -5.10990324 + -3.333333334 = -8.443236574
w = -8.443236574

Simplifying
w = -8.443236574


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.776569906, -8.443236574}

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