2x^2-x=91

Solution for 2x^2-x=91 equation:

Simplifying
2x2 + -1x = 91

Reorder the terms:
-1x + 2x2 = 91

Solving
-1x + 2x2 = 91

Solving for variable 'x'.

Reorder the terms:
-91 + -1x + 2x2 = 91 + -91

Combine like terms: 91 + -91 = 0
-91 + -1x + 2x2 = 0

Factor a trinomial.
(-13 + -2x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-13 + -2x)' equal to zero and attempt to solve:

Simplifying
-13 + -2x = 0

Solving
-13 + -2x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -2x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2x = 0 + 13
-2x = 0 + 13

Combine like terms: 0 + 13 = 13
-2x = 13

Divide each side by '-2'.
x = -6.5

Simplifying
x = -6.5
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-6.5, 7}