2x^2-61=x^2-12

Solution for 2x^2-61=x^2-12 equation:

Simplifying
2x2 + -61 = x2 + -12

Reorder the terms:
-61 + 2x2 = x2 + -12

Reorder the terms:
-61 + 2x2 = -12 + x2

Solving
-61 + 2x2 = -12 + 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.
-61 + 2x2 + -1x2 = -12 + x2 + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-61 + 1x2 = -12 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-61 + 1x2 = -12 + 0
-61 + 1x2 = -12

Add '61' to each side of the equation.
-61 + 61 + 1x2 = -12 + 61

Combine like terms: -61 + 61 = 0
0 + 1x2 = -12 + 61
1x2 = -12 + 61

Combine like terms: -12 + 61 = 49
1x2 = 49

Divide each side by '1'.
x2 = 49

Simplifying
x2 = 49

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