5w^2=3w+6

Solution for 5w^2=3w+6 equation:

Simplifying
5w2 = 3w + 6

Reorder the terms:
5w2 = 6 + 3w

Solving
5w2 = 6 + 3w

Solving for variable 'w'.

Reorder the terms:
-6 + -3w + 5w2 = 6 + 3w + -6 + -3w

Reorder the terms:
-6 + -3w + 5w2 = 6 + -6 + 3w + -3w

Combine like terms: 6 + -6 = 0
-6 + -3w + 5w2 = 0 + 3w + -3w
-6 + -3w + 5w2 = 3w + -3w

Combine like terms: 3w + -3w = 0
-6 + -3w + 5w2 = 0

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

Divide each side by '5'.
-1.2 + -0.6w + w2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -0.6w + 1.2 + w2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -0.6w + w2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -0.6w + w2 = 0 + 1.2
-0.6w + w2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-0.6w + w2 = 1.2

The w term is -0.6w.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6w + 0.09 + w2 = 1.2 + 0.09

Reorder the terms:
0.09 + -0.6w + w2 = 1.2 + 0.09

Combine like terms: 1.2 + 0.09 = 1.29
0.09 + -0.6w + w2 = 1.29

Factor a perfect square on the left side:
(w + -0.3)(w + -0.3) = 1.29

Calculate the square root of the right side: 1.135781669

Break this problem into two subproblems by setting 
(w + -0.3) equal to 1.135781669 and -1.135781669.

Subproblem 1
w + -0.3 = 1.135781669

Simplifying
w + -0.3 = 1.135781669

Reorder the terms:
-0.3 + w = 1.135781669

Solving
-0.3 + w = 1.135781669

Solving for variable 'w'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + w = 1.135781669 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + w = 1.135781669 + 0.3
w = 1.135781669 + 0.3

Combine like terms: 1.135781669 + 0.3 = 1.435781669
w = 1.435781669

Simplifying
w = 1.435781669

Subproblem 2
w + -0.3 = -1.135781669

Simplifying
w + -0.3 = -1.135781669

Reorder the terms:
-0.3 + w = -1.135781669

Solving
-0.3 + w = -1.135781669

Solving for variable 'w'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + w = -1.135781669 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + w = -1.135781669 + 0.3
w = -1.135781669 + 0.3

Combine like terms: -1.135781669 + 0.3 = -0.835781669
w = -0.835781669

Simplifying
w = -0.835781669

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.435781669, -0.835781669}