2x^2-1=9x+17

Solution for 2x^2-1=9x+17 equation:

Simplifying
2x2 + -1 = 9x + 17

Reorder the terms:
-1 + 2x2 = 9x + 17

Reorder the terms:
-1 + 2x2 = 17 + 9x

Solving
-1 + 2x2 = 17 + 9x

Solving for variable 'x'.

Reorder the terms:
-1 + -17 + -9x + 2x2 = 17 + 9x + -17 + -9x

Combine like terms: -1 + -17 = -18
-18 + -9x + 2x2 = 17 + 9x + -17 + -9x

Reorder the terms:
-18 + -9x + 2x2 = 17 + -17 + 9x + -9x

Combine like terms: 17 + -17 = 0
-18 + -9x + 2x2 = 0 + 9x + -9x
-18 + -9x + 2x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-18 + -9x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5
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 = {-1.5, 6}