0=6x^2-x-51

Solution for 0=6x^2-x-51 equation:

Simplifying
0 = 6x2 + -1x + -51

Reorder the terms:
0 = -51 + -1x + 6x2

Solving
0 = -51 + -1x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + 51 = 51
51 + x + -6x2 = -51 + -1x + 6x2 + 51 + x + -6x2

Reorder the terms:
51 + x + -6x2 = -51 + 51 + -1x + x + 6x2 + -6x2

Combine like terms: -51 + 51 = 0
51 + x + -6x2 = 0 + -1x + x + 6x2 + -6x2
51 + x + -6x2 = -1x + x + 6x2 + -6x2

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

Combine like terms: 6x2 + -6x2 = 0
51 + x + -6x2 = 0

Factor a trinomial.
(3 + -1x)(17 + 6x) = 0

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(17 + 6x)' equal to zero and attempt to solve:

Simplifying
17 + 6x = 0

Solving
17 + 6x = 0

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

Add '-17' to each side of the equation.
17 + -17 + 6x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 6x = 0 + -17
6x = 0 + -17

Combine like terms: 0 + -17 = -17
6x = -17

Divide each side by '6'.
x = -2.833333333

Simplifying
x = -2.833333333
Solution
x = {3, -2.833333333}