5w=10w^2+15

Solution for 5w=10w^2+15 equation:

Simplifying
5w = 10w2 + 15

Reorder the terms:
5w = 15 + 10w2

Solving
5w = 15 + 10w2

Solving for variable 'w'.

Reorder the terms:
-15 + 5w + -10w2 = 15 + 10w2 + -15 + -10w2

Reorder the terms:
-15 + 5w + -10w2 = 15 + -15 + 10w2 + -10w2

Combine like terms: 15 + -15 = 0
-15 + 5w + -10w2 = 0 + 10w2 + -10w2
-15 + 5w + -10w2 = 10w2 + -10w2

Combine like terms: 10w2 + -10w2 = 0
-15 + 5w + -10w2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + w + -2w2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-3 + w + -2w2)' equal to zero and attempt to solve:

Simplifying
-3 + w + -2w2 = 0

Solving
-3 + w + -2w2 = 0

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

Divide each side by '-2'.
1.5 + -0.5w + w2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -0.5w + -1.5 + w2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -0.5w + w2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -0.5w + w2 = 0 + -1.5
-0.5w + w2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-0.5w + w2 = -1.5

The w term is w.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.5w + 0.25 + w2 = -1.5 + 0.25

Reorder the terms:
0.25 + -0.5w + w2 = -1.5 + 0.25

Combine like terms: -1.5 + 0.25 = -1.25
0.25 + -0.5w + w2 = -1.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = -1.25

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.