1233.88=-2.06x^2+77.84x+743

Solution for 1233.88=-2.06x^2+77.84x+743 equation:

Simplifying
1233.88 = -2.06x2 + 77.84x + 743

Reorder the terms:
1233.88 = 743 + 77.84x + -2.06x2

Solving
1233.88 = 743 + 77.84x + -2.06x2

Solving for variable 'x'.

Combine like terms: 1233.88 + -743 = 490.88
490.88 + -77.84x + 2.06x2 = 743 + 77.84x + -2.06x2 + -743 + -77.84x + 2.06x2

Reorder the terms:
490.88 + -77.84x + 2.06x2 = 743 + -743 + 77.84x + -77.84x + -2.06x2 + 2.06x2

Combine like terms: 743 + -743 = 0
490.88 + -77.84x + 2.06x2 = 0 + 77.84x + -77.84x + -2.06x2 + 2.06x2
490.88 + -77.84x + 2.06x2 = 77.84x + -77.84x + -2.06x2 + 2.06x2

Combine like terms: 77.84x + -77.84x = 0.00
490.88 + -77.84x + 2.06x2 = 0.00 + -2.06x2 + 2.06x2
490.88 + -77.84x + 2.06x2 = -2.06x2 + 2.06x2

Combine like terms: -2.06x2 + 2.06x2 = 0.00
490.88 + -77.84x + 2.06x2 = 0.00

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

Divide each side by '2.06'.
238.2912621 + -37.78640777x + x2 = 0

Move the constant term to the right:

Add '-238.2912621' to each side of the equation.
238.2912621 + -37.78640777x + -238.2912621 + x2 = 0 + -238.2912621

Reorder the terms:
238.2912621 + -238.2912621 + -37.78640777x + x2 = 0 + -238.2912621

Combine like terms: 238.2912621 + -238.2912621 = 0.0000000
0.0000000 + -37.78640777x + x2 = 0 + -238.2912621
-37.78640777x + x2 = 0 + -238.2912621

Combine like terms: 0 + -238.2912621 = -238.2912621
-37.78640777x + x2 = -238.2912621

The x term is -37.78640777x.  Take half its coefficient (-18.89320389).
Square it (356.9531532) and add it to both sides.

Add '356.9531532' to each side of the equation.
-37.78640777x + 356.9531532 + x2 = -238.2912621 + 356.9531532

Reorder the terms:
356.9531532 + -37.78640777x + x2 = -238.2912621 + 356.9531532

Combine like terms: -238.2912621 + 356.9531532 = 118.6618911
356.9531532 + -37.78640777x + x2 = 118.6618911

Factor a perfect square on the left side:
(x + -18.89320389)(x + -18.89320389) = 118.6618911

Calculate the square root of the right side: 10.893203895

Break this problem into two subproblems by setting 
(x + -18.89320389) equal to 10.893203895 and -10.893203895.

Subproblem 1
x + -18.89320389 = 10.893203895

Simplifying
x + -18.89320389 = 10.893203895

Reorder the terms:
-18.89320389 + x = 10.893203895

Solving
-18.89320389 + x = 10.893203895

Solving for variable 'x'.

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

Add '18.89320389' to each side of the equation.
-18.89320389 + 18.89320389 + x = 10.893203895 + 18.89320389

Combine like terms: -18.89320389 + 18.89320389 = 0.00000000
0.00000000 + x = 10.893203895 + 18.89320389
x = 10.893203895 + 18.89320389

Combine like terms: 10.893203895 + 18.89320389 = 29.786407785
x = 29.786407785

Simplifying
x = 29.786407785

Subproblem 2
x + -18.89320389 = -10.893203895

Simplifying
x + -18.89320389 = -10.893203895

Reorder the terms:
-18.89320389 + x = -10.893203895

Solving
-18.89320389 + x = -10.893203895

Solving for variable 'x'.

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

Add '18.89320389' to each side of the equation.
-18.89320389 + 18.89320389 + x = -10.893203895 + 18.89320389

Combine like terms: -18.89320389 + 18.89320389 = 0.00000000
0.00000000 + x = -10.893203895 + 18.89320389
x = -10.893203895 + 18.89320389

Combine like terms: -10.893203895 + 18.89320389 = 7.999999995
x = 7.999999995

Simplifying
x = 7.999999995

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {29.786407785, 7.999999995}