0.5*x^2-1.5=3

Solution for 0.5*x^2-1.5=3 equation:

Simplifying
0.5x2 + -1.5 = 3

Reorder the terms:
-1.5 + 0.5x2 = 3

Solving
-1.5 + 0.5x2 = 3

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + 0.5x2 = 3 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 0.5x2 = 3 + 1.5
0.5x2 = 3 + 1.5

Combine like terms: 3 + 1.5 = 4.5
0.5x2 = 4.5

Divide each side by '0.5'.
x2 = 9

Simplifying
x2 = 9

Take the square root of each side:
x = {-3, 3}