23423x-90x^2=90

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

Simplifying
23423x + -90x2 = 90

Solving
23423x + -90x2 = 90

Solving for variable 'x'.

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

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

Begin completing the square.  Divide all terms by
-90 the coefficient of the squared term: 

Divide each side by '-90'.
1 + -260.2555556x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -260.2555556x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -260.2555556x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -260.2555556x + x2 = 0 + -1
-260.2555556x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-260.2555556x + x2 = -1

The x term is -260.2555556x.  Take half its coefficient (-130.1277778).
Square it (16933.23856) and add it to both sides.

Add '16933.23856' to each side of the equation.
-260.2555556x + 16933.23856 + x2 = -1 + 16933.23856

Reorder the terms:
16933.23856 + -260.2555556x + x2 = -1 + 16933.23856

Combine like terms: -1 + 16933.23856 = 16932.23856
16933.23856 + -260.2555556x + x2 = 16932.23856

Factor a perfect square on the left side:
(x + -130.1277778)(x + -130.1277778) = 16932.23856

Calculate the square root of the right side: 130.123935385

Break this problem into two subproblems by setting 
(x + -130.1277778) equal to 130.123935385 and -130.123935385.

Subproblem 1
x + -130.1277778 = 130.123935385

Simplifying
x + -130.1277778 = 130.123935385

Reorder the terms:
-130.1277778 + x = 130.123935385

Solving
-130.1277778 + x = 130.123935385

Solving for variable 'x'.

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

Add '130.1277778' to each side of the equation.
-130.1277778 + 130.1277778 + x = 130.123935385 + 130.1277778

Combine like terms: -130.1277778 + 130.1277778 = 0.0000000
0.0000000 + x = 130.123935385 + 130.1277778
x = 130.123935385 + 130.1277778

Combine like terms: 130.123935385 + 130.1277778 = 260.251713185
x = 260.251713185

Simplifying
x = 260.251713185

Subproblem 2
x + -130.1277778 = -130.123935385

Simplifying
x + -130.1277778 = -130.123935385

Reorder the terms:
-130.1277778 + x = -130.123935385

Solving
-130.1277778 + x = -130.123935385

Solving for variable 'x'.

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

Add '130.1277778' to each side of the equation.
-130.1277778 + 130.1277778 + x = -130.123935385 + 130.1277778

Combine like terms: -130.1277778 + 130.1277778 = 0.0000000
0.0000000 + x = -130.123935385 + 130.1277778
x = -130.123935385 + 130.1277778

Combine like terms: -130.123935385 + 130.1277778 = 0.003842415
x = 0.003842415

Simplifying
x = 0.003842415

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {260.251713185, 0.003842415}