234x-(2343-90)*x^2=90x-90

Solution for 234x-(2343-90)*x^2=90x-90 equation:

Simplifying
234x + -1(2343 + -90) * x2 = 90x + -90

Combine like terms: 2343 + -90 = 2253
234x + -1(2253) * x2 = 90x + -90

Multiply -1 * 2253
234x + -2253x2 = 90x + -90

Reorder the terms:
234x + -2253x2 = -90 + 90x

Solving
234x + -2253x2 = -90 + 90x

Solving for variable 'x'.

Reorder the terms:
90 + 234x + -90x + -2253x2 = -90 + 90x + 90 + -90x

Combine like terms: 234x + -90x = 144x
90 + 144x + -2253x2 = -90 + 90x + 90 + -90x

Reorder the terms:
90 + 144x + -2253x2 = -90 + 90 + 90x + -90x

Combine like terms: -90 + 90 = 0
90 + 144x + -2253x2 = 0 + 90x + -90x
90 + 144x + -2253x2 = 90x + -90x

Combine like terms: 90x + -90x = 0
90 + 144x + -2253x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(30 + 48x + -751x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(30 + 48x + -751x2)' equal to zero and attempt to solve:

Simplifying
30 + 48x + -751x2 = 0

Solving
30 + 48x + -751x2 = 0

Begin completing the square.  Divide all terms by
-751 the coefficient of the squared term: 

Divide each side by '-751'.
-0.03994673768 + -0.06391478029x + x2 = 0

Move the constant term to the right:

Add '0.03994673768' to each side of the equation.
-0.03994673768 + -0.06391478029x + 0.03994673768 + x2 = 0 + 0.03994673768

Reorder the terms:
-0.03994673768 + 0.03994673768 + -0.06391478029x + x2 = 0 + 0.03994673768

Combine like terms: -0.03994673768 + 0.03994673768 = 0.00000000000
0.00000000000 + -0.06391478029x + x2 = 0 + 0.03994673768
-0.06391478029x + x2 = 0 + 0.03994673768

Combine like terms: 0 + 0.03994673768 = 0.03994673768
-0.06391478029x + x2 = 0.03994673768

The x term is -0.06391478029x.  Take half its coefficient (-0.03195739015).
Square it (0.001021274785) and add it to both sides.

Add '0.001021274785' to each side of the equation.
-0.06391478029x + 0.001021274785 + x2 = 0.03994673768 + 0.001021274785

Reorder the terms:
0.001021274785 + -0.06391478029x + x2 = 0.03994673768 + 0.001021274785

Combine like terms: 0.03994673768 + 0.001021274785 = 0.040968012465
0.001021274785 + -0.06391478029x + x2 = 0.040968012465

Factor a perfect square on the left side:
(x + -0.03195739015)(x + -0.03195739015) = 0.040968012465

Calculate the square root of the right side: 0.202405564

Break this problem into two subproblems by setting 
(x + -0.03195739015) equal to 0.202405564 and -0.202405564.

Subproblem 1
x + -0.03195739015 = 0.202405564

Simplifying
x + -0.03195739015 = 0.202405564

Reorder the terms:
-0.03195739015 + x = 0.202405564

Solving
-0.03195739015 + x = 0.202405564

Solving for variable 'x'.

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

Add '0.03195739015' to each side of the equation.
-0.03195739015 + 0.03195739015 + x = 0.202405564 + 0.03195739015

Combine like terms: -0.03195739015 + 0.03195739015 = 0.00000000000
0.00000000000 + x = 0.202405564 + 0.03195739015
x = 0.202405564 + 0.03195739015

Combine like terms: 0.202405564 + 0.03195739015 = 0.23436295415
x = 0.23436295415

Simplifying
x = 0.23436295415

Subproblem 2
x + -0.03195739015 = -0.202405564

Simplifying
x + -0.03195739015 = -0.202405564

Reorder the terms:
-0.03195739015 + x = -0.202405564

Solving
-0.03195739015 + x = -0.202405564

Solving for variable 'x'.

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

Add '0.03195739015' to each side of the equation.
-0.03195739015 + 0.03195739015 + x = -0.202405564 + 0.03195739015

Combine like terms: -0.03195739015 + 0.03195739015 = 0.00000000000
0.00000000000 + x = -0.202405564 + 0.03195739015
x = -0.202405564 + 0.03195739015

Combine like terms: -0.202405564 + 0.03195739015 = -0.17044817385
x = -0.17044817385

Simplifying
x = -0.17044817385

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.23436295415, -0.17044817385}
Solution
x = {0.23436295415, -0.17044817385}