3x^2-83=15+x^2

Solution for 3x^2-83=15+x^2 equation:

Simplifying
3x2 + -83 = 15 + x2

Reorder the terms:
-83 + 3x2 = 15 + x2

Solving
-83 + 3x2 = 15 + x2

Solving for variable 'x'.

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

Add '-1x2' to each side of the equation.
-83 + 3x2 + -1x2 = 15 + x2 + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-83 + 2x2 = 15 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-83 + 2x2 = 15 + 0
-83 + 2x2 = 15

Add '83' to each side of the equation.
-83 + 83 + 2x2 = 15 + 83

Combine like terms: -83 + 83 = 0
0 + 2x2 = 15 + 83
2x2 = 15 + 83

Combine like terms: 15 + 83 = 98
2x2 = 98

Divide each side by '2'.
x2 = 49

Simplifying
x2 = 49

Take the square root of each side:
x = {-7, 7}