3x^2+x=114

Solution for 3x^2+x=114 equation:

Simplifying
3x2 + x = 114

Reorder the terms:
x + 3x2 = 114

Solving
x + 3x2 = 114

Solving for variable 'x'.

Reorder the terms:
-114 + x + 3x2 = 114 + -114

Combine like terms: 114 + -114 = 0
-114 + x + 3x2 = 0

Factor a trinomial.
(-19 + -3x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-19 + -3x)' equal to zero and attempt to solve:

Simplifying
-19 + -3x = 0

Solving
-19 + -3x = 0

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

Add '19' to each side of the equation.
-19 + 19 + -3x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -3x = 0 + 19
-3x = 0 + 19

Combine like terms: 0 + 19 = 19
-3x = 19

Divide each side by '-3'.
x = -6.333333333

Simplifying
x = -6.333333333
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-6.333333333, 6}