23423x^2-90=90-89x

Solution for 23423x^2-90=90-89x equation:

Simplifying
23423x2 + -90 = 90 + -89x

Reorder the terms:
-90 + 23423x2 = 90 + -89x

Solving
-90 + 23423x2 = 90 + -89x

Solving for variable 'x'.

Reorder the terms:
-90 + -90 + 89x + 23423x2 = 90 + -89x + -90 + 89x

Combine like terms: -90 + -90 = -180
-180 + 89x + 23423x2 = 90 + -89x + -90 + 89x

Reorder the terms:
-180 + 89x + 23423x2 = 90 + -90 + -89x + 89x

Combine like terms: 90 + -90 = 0
-180 + 89x + 23423x2 = 0 + -89x + 89x
-180 + 89x + 23423x2 = -89x + 89x

Combine like terms: -89x + 89x = 0
-180 + 89x + 23423x2 = 0

Begin completing the square.  Divide all terms by
23423 the coefficient of the squared term: 

Divide each side by '23423'.
-0.007684754301 + 0.003799684071x + x2 = 0

Move the constant term to the right:

Add '0.007684754301' to each side of the equation.
-0.007684754301 + 0.003799684071x + 0.007684754301 + x2 = 0 + 0.007684754301

Reorder the terms:
-0.007684754301 + 0.007684754301 + 0.003799684071x + x2 = 0 + 0.007684754301

Combine like terms: -0.007684754301 + 0.007684754301 = 0.000000000000
0.000000000000 + 0.003799684071x + x2 = 0 + 0.007684754301
0.003799684071x + x2 = 0 + 0.007684754301

Combine like terms: 0 + 0.007684754301 = 0.007684754301
0.003799684071x + x2 = 0.007684754301

The x term is 0.003799684071x.  Take half its coefficient (0.001899842036).
Square it (0.000003609399762) and add it to both sides.

Add '0.000003609399762' to each side of the equation.
0.003799684071x + 0.000003609399762 + x2 = 0.007684754301 + 0.000003609399762

Reorder the terms:
0.000003609399762 + 0.003799684071x + x2 = 0.007684754301 + 0.000003609399762

Combine like terms: 0.007684754301 + 0.000003609399762 = 0.007688363700762
0.000003609399762 + 0.003799684071x + x2 = 0.007688363700762

Factor a perfect square on the left side:
(x + 0.001899842036)(x + 0.001899842036) = 0.007688363700762

Calculate the square root of the right side: 0.087683315

Break this problem into two subproblems by setting 
(x + 0.001899842036) equal to 0.087683315 and -0.087683315.

Subproblem 1
x + 0.001899842036 = 0.087683315

Simplifying
x + 0.001899842036 = 0.087683315

Reorder the terms:
0.001899842036 + x = 0.087683315

Solving
0.001899842036 + x = 0.087683315

Solving for variable 'x'.

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

Add '-0.001899842036' to each side of the equation.
0.001899842036 + -0.001899842036 + x = 0.087683315 + -0.001899842036

Combine like terms: 0.001899842036 + -0.001899842036 = 0.000000000000
0.000000000000 + x = 0.087683315 + -0.001899842036
x = 0.087683315 + -0.001899842036

Combine like terms: 0.087683315 + -0.001899842036 = 0.085783472964
x = 0.085783472964

Simplifying
x = 0.085783472964

Subproblem 2
x + 0.001899842036 = -0.087683315

Simplifying
x + 0.001899842036 = -0.087683315

Reorder the terms:
0.001899842036 + x = -0.087683315

Solving
0.001899842036 + x = -0.087683315

Solving for variable 'x'.

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

Add '-0.001899842036' to each side of the equation.
0.001899842036 + -0.001899842036 + x = -0.087683315 + -0.001899842036

Combine like terms: 0.001899842036 + -0.001899842036 = 0.000000000000
0.000000000000 + x = -0.087683315 + -0.001899842036
x = -0.087683315 + -0.001899842036

Combine like terms: -0.087683315 + -0.001899842036 = -0.089583157036
x = -0.089583157036

Simplifying
x = -0.089583157036

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.085783472964, -0.089583157036}