2x^2-19x+51=6

Solution for 2x^2-19x+51=6 equation:

Simplifying
2x2 + -19x + 51 = 6

Reorder the terms:
51 + -19x + 2x2 = 6

Solving
51 + -19x + 2x2 = 6

Solving for variable 'x'.

Reorder the terms:
51 + -6 + -19x + 2x2 = 6 + -6

Combine like terms: 51 + -6 = 45
45 + -19x + 2x2 = 6 + -6

Combine like terms: 6 + -6 = 0
45 + -19x + 2x2 = 0

Factor a trinomial.
(9 + -2x)(5 + -1x) = 0

Subproblem 1
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {4.5, 5}