6x^2-51=x

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

Simplifying
6x2 + -51 = x

Reorder the terms:
-51 + 6x2 = x

Solving
-51 + 6x2 = x

Solving for variable 'x'.

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

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

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {-2.833333333, 3}