4x^2-5=-.5x^2

Solution for 4x^2-5=-.5x^2 equation:

Simplifying
4x2 + -5 = -0.5x2

Reorder the terms:
-5 + 4x2 = -0.5x2

Solving
-5 + 4x2 = -0.5x2

Solving for variable 'x'.

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

Add '0.5x2' to each side of the equation.
-5 + 4x2 + 0.5x2 = -0.5x2 + 0.5x2

Combine like terms: 4x2 + 0.5x2 = 4.5x2
-5 + 4.5x2 = -0.5x2 + 0.5x2

Combine like terms: -0.5x2 + 0.5x2 = 0.0
-5 + 4.5x2 = 0.0

Add '5' to each side of the equation.
-5 + 5 + 4.5x2 = 0.0 + 5

Combine like terms: -5 + 5 = 0
0 + 4.5x2 = 0.0 + 5
4.5x2 = 0.0 + 5

Combine like terms: 0.0 + 5 = 5
4.5x2 = 5

Divide each side by '4.5'.
x2 = 1.111111111

Simplifying
x2 = 1.111111111

Take the square root of each side:
x = {-1.054092553, 1.054092553}