185709=910x-x^2

Solution for 185709=910x-x^2 equation:

Simplifying
185709 = 910x + -1x2

Solving
185709 = 910x + -1x2

Solving for variable 'x'.

Reorder the terms:
185709 + -910x + x2 = 910x + -910x + -1x2 + x2

Combine like terms: 910x + -910x = 0
185709 + -910x + x2 = 0 + -1x2 + x2
185709 + -910x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
185709 + -910x + x2 = 0

Factor a trinomial.
(309 + -1x)(601 + -1x) = 0

Subproblem 1
Set the factor '(309 + -1x)' equal to zero and attempt to solve:

Simplifying
309 + -1x = 0

Solving
309 + -1x = 0

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

Add '-309' to each side of the equation.
309 + -309 + -1x = 0 + -309

Combine like terms: 309 + -309 = 0
0 + -1x = 0 + -309
-1x = 0 + -309

Combine like terms: 0 + -309 = -309
-1x = -309

Divide each side by '-1'.
x = 309

Simplifying
x = 309
Subproblem 2
Set the factor '(601 + -1x)' equal to zero and attempt to solve:

Simplifying
601 + -1x = 0

Solving
601 + -1x = 0

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

Add '-601' to each side of the equation.
601 + -601 + -1x = 0 + -601

Combine like terms: 601 + -601 = 0
0 + -1x = 0 + -601
-1x = 0 + -601

Combine like terms: 0 + -601 = -601
-1x = -601

Divide each side by '-1'.
x = 601

Simplifying
x = 601
Solution
x = {309, 601}