x^2=x+90

Solution for x^2=x+90 equation:

Simplifying
x2 = x + 90

Reorder the terms:
x2 = 90 + x

Solving
x2 = 90 + x

Solving for variable 'x'.

Reorder the terms:
-90 + -1x + x2 = 90 + x + -90 + -1x

Reorder the terms:
-90 + -1x + x2 = 90 + -90 + x + -1x

Combine like terms: 90 + -90 = 0
-90 + -1x + x2 = 0 + x + -1x
-90 + -1x + x2 = x + -1x

Combine like terms: x + -1x = 0
-90 + -1x + x2 = 0

Factor a trinomial.
(-9 + -1x)(10 + -1x) = 0

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

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 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 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-9, 10}