w^2+1=3w^2-2

Solution for w^2+1=3w^2-2 equation:

Simplifying
w2 + 1 = 3w2 + -2

Reorder the terms:
1 + w2 = 3w2 + -2

Reorder the terms:
1 + w2 = -2 + 3w2

Solving
1 + w2 = -2 + 3w2

Solving for variable 'w'.

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

Add '-3w2' to each side of the equation.
1 + w2 + -3w2 = -2 + 3w2 + -3w2

Combine like terms: w2 + -3w2 = -2w2
1 + -2w2 = -2 + 3w2 + -3w2

Combine like terms: 3w2 + -3w2 = 0
1 + -2w2 = -2 + 0
1 + -2w2 = -2

Add '-1' to each side of the equation.
1 + -1 + -2w2 = -2 + -1

Combine like terms: 1 + -1 = 0
0 + -2w2 = -2 + -1
-2w2 = -2 + -1

Combine like terms: -2 + -1 = -3
-2w2 = -3

Divide each side by '-2'.
w2 = 1.5

Simplifying
w2 = 1.5

Take the square root of each side:
w = {-1.224744871, 1.224744871}