3x^2+x+6=x^2+x+42

Solution for 3x^2+x+6=x^2+x+42 equation:

Simplifying
3x2 + x + 6 = x2 + x + 42

Reorder the terms:
6 + x + 3x2 = x2 + x + 42

Reorder the terms:
6 + x + 3x2 = 42 + x + x2

Add '-1x' to each side of the equation.
6 + x + -1x + 3x2 = 42 + x + -1x + x2

Combine like terms: x + -1x = 0
6 + 0 + 3x2 = 42 + x + -1x + x2
6 + 3x2 = 42 + x + -1x + x2

Combine like terms: x + -1x = 0
6 + 3x2 = 42 + 0 + x2
6 + 3x2 = 42 + x2

Solving
6 + 3x2 = 42 + 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.
6 + 3x2 + -1x2 = 42 + x2 + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
6 + 2x2 = 42 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + 2x2 = 42 + 0
6 + 2x2 = 42

Add '-6' to each side of the equation.
6 + -6 + 2x2 = 42 + -6

Combine like terms: 6 + -6 = 0
0 + 2x2 = 42 + -6
2x2 = 42 + -6

Combine like terms: 42 + -6 = 36
2x2 = 36

Divide each side by '2'.
x2 = 18

Simplifying
x2 = 18

Take the square root of each side:
x = {-4.242640687, 4.242640687}