1234+86x*24x=345*54x+56

Solution for 1234+86x*24x=345*54x+56 equation:

Simplifying
1234 + 86x * 24x = 345 * 54x + 56

Reorder the terms for easier multiplication:
1234 + 86 * 24x * x = 345 * 54x + 56

Multiply 86 * 24
1234 + 2064x * x = 345 * 54x + 56

Multiply x * x
1234 + 2064x2 = 345 * 54x + 56

Multiply 345 * 54
1234 + 2064x2 = 18630x + 56

Reorder the terms:
1234 + 2064x2 = 56 + 18630x

Solving
1234 + 2064x2 = 56 + 18630x

Solving for variable 'x'.

Reorder the terms:
1234 + -56 + -18630x + 2064x2 = 56 + 18630x + -56 + -18630x

Combine like terms: 1234 + -56 = 1178
1178 + -18630x + 2064x2 = 56 + 18630x + -56 + -18630x

Reorder the terms:
1178 + -18630x + 2064x2 = 56 + -56 + 18630x + -18630x

Combine like terms: 56 + -56 = 0
1178 + -18630x + 2064x2 = 0 + 18630x + -18630x
1178 + -18630x + 2064x2 = 18630x + -18630x

Combine like terms: 18630x + -18630x = 0
1178 + -18630x + 2064x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(589 + -9315x + 1032x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(589 + -9315x + 1032x2)' equal to zero and attempt to solve:

Simplifying
589 + -9315x + 1032x2 = 0

Solving
589 + -9315x + 1032x2 = 0

Begin completing the square.  Divide all terms by
1032 the coefficient of the squared term: 

Divide each side by '1032'.
0.5707364341 + -9.026162791x + x2 = 0

Move the constant term to the right:

Add '-0.5707364341' to each side of the equation.
0.5707364341 + -9.026162791x + -0.5707364341 + x2 = 0 + -0.5707364341

Reorder the terms:
0.5707364341 + -0.5707364341 + -9.026162791x + x2 = 0 + -0.5707364341

Combine like terms: 0.5707364341 + -0.5707364341 = 0.0000000000
0.0000000000 + -9.026162791x + x2 = 0 + -0.5707364341
-9.026162791x + x2 = 0 + -0.5707364341

Combine like terms: 0 + -0.5707364341 = -0.5707364341
-9.026162791x + x2 = -0.5707364341

The x term is -9.026162791x.  Take half its coefficient (-4.513081396).
Square it (20.36790369) and add it to both sides.

Add '20.36790369' to each side of the equation.
-9.026162791x + 20.36790369 + x2 = -0.5707364341 + 20.36790369

Reorder the terms:
20.36790369 + -9.026162791x + x2 = -0.5707364341 + 20.36790369

Combine like terms: -0.5707364341 + 20.36790369 = 19.7971672559
20.36790369 + -9.026162791x + x2 = 19.7971672559

Factor a perfect square on the left side:
(x + -4.513081396)(x + -4.513081396) = 19.7971672559

Calculate the square root of the right side: 4.449400775

Break this problem into two subproblems by setting 
(x + -4.513081396) equal to 4.449400775 and -4.449400775.

Subproblem 1
x + -4.513081396 = 4.449400775

Simplifying
x + -4.513081396 = 4.449400775

Reorder the terms:
-4.513081396 + x = 4.449400775

Solving
-4.513081396 + x = 4.449400775

Solving for variable 'x'.

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

Add '4.513081396' to each side of the equation.
-4.513081396 + 4.513081396 + x = 4.449400775 + 4.513081396

Combine like terms: -4.513081396 + 4.513081396 = 0.000000000
0.000000000 + x = 4.449400775 + 4.513081396
x = 4.449400775 + 4.513081396

Combine like terms: 4.449400775 + 4.513081396 = 8.962482171
x = 8.962482171

Simplifying
x = 8.962482171

Subproblem 2
x + -4.513081396 = -4.449400775

Simplifying
x + -4.513081396 = -4.449400775

Reorder the terms:
-4.513081396 + x = -4.449400775

Solving
-4.513081396 + x = -4.449400775

Solving for variable 'x'.

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

Add '4.513081396' to each side of the equation.
-4.513081396 + 4.513081396 + x = -4.449400775 + 4.513081396

Combine like terms: -4.513081396 + 4.513081396 = 0.000000000
0.000000000 + x = -4.449400775 + 4.513081396
x = -4.449400775 + 4.513081396

Combine like terms: -4.449400775 + 4.513081396 = 0.063680621
x = 0.063680621

Simplifying
x = 0.063680621

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.962482171, 0.063680621}
Solution
x = {8.962482171, 0.063680621}