2x+7.43=-0.21x^2-0.84x+50

Solution for 2x+7.43=-0.21x^2-0.84x+50 equation:

Simplifying
2x + 7.43 = -0.21x2 + -0.84x + 50

Reorder the terms:
7.43 + 2x = -0.21x2 + -0.84x + 50

Reorder the terms:
7.43 + 2x = 50 + -0.84x + -0.21x2

Solving
7.43 + 2x = 50 + -0.84x + -0.21x2

Solving for variable 'x'.

Reorder the terms:
7.43 + -50 + 2x + 0.84x + 0.21x2 = 50 + -0.84x + -0.21x2 + -50 + 0.84x + 0.21x2

Combine like terms: 7.43 + -50 = -42.57
-42.57 + 2x + 0.84x + 0.21x2 = 50 + -0.84x + -0.21x2 + -50 + 0.84x + 0.21x2

Combine like terms: 2x + 0.84x = 2.84x
-42.57 + 2.84x + 0.21x2 = 50 + -0.84x + -0.21x2 + -50 + 0.84x + 0.21x2

Reorder the terms:
-42.57 + 2.84x + 0.21x2 = 50 + -50 + -0.84x + 0.84x + -0.21x2 + 0.21x2

Combine like terms: 50 + -50 = 0
-42.57 + 2.84x + 0.21x2 = 0 + -0.84x + 0.84x + -0.21x2 + 0.21x2
-42.57 + 2.84x + 0.21x2 = -0.84x + 0.84x + -0.21x2 + 0.21x2

Combine like terms: -0.84x + 0.84x = 0.00
-42.57 + 2.84x + 0.21x2 = 0.00 + -0.21x2 + 0.21x2
-42.57 + 2.84x + 0.21x2 = -0.21x2 + 0.21x2

Combine like terms: -0.21x2 + 0.21x2 = 0.00
-42.57 + 2.84x + 0.21x2 = 0.00

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

Divide each side by '0.21'.
-202.7142857 + 13.52380952x + x2 = 0

Move the constant term to the right:

Add '202.7142857' to each side of the equation.
-202.7142857 + 13.52380952x + 202.7142857 + x2 = 0 + 202.7142857

Reorder the terms:
-202.7142857 + 202.7142857 + 13.52380952x + x2 = 0 + 202.7142857

Combine like terms: -202.7142857 + 202.7142857 = 0.0000000
0.0000000 + 13.52380952x + x2 = 0 + 202.7142857
13.52380952x + x2 = 0 + 202.7142857

Combine like terms: 0 + 202.7142857 = 202.7142857
13.52380952x + x2 = 202.7142857

The x term is 13.52380952x.  Take half its coefficient (6.76190476).
Square it (45.72335598) and add it to both sides.

Add '45.72335598' to each side of the equation.
13.52380952x + 45.72335598 + x2 = 202.7142857 + 45.72335598

Reorder the terms:
45.72335598 + 13.52380952x + x2 = 202.7142857 + 45.72335598

Combine like terms: 202.7142857 + 45.72335598 = 248.43764168
45.72335598 + 13.52380952x + x2 = 248.43764168

Factor a perfect square on the left side:
(x + 6.76190476)(x + 6.76190476) = 248.43764168

Calculate the square root of the right side: 15.761904761

Break this problem into two subproblems by setting 
(x + 6.76190476) equal to 15.761904761 and -15.761904761.

Subproblem 1
x + 6.76190476 = 15.761904761

Simplifying
x + 6.76190476 = 15.761904761

Reorder the terms:
6.76190476 + x = 15.761904761

Solving
6.76190476 + x = 15.761904761

Solving for variable 'x'.

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

Add '-6.76190476' to each side of the equation.
6.76190476 + -6.76190476 + x = 15.761904761 + -6.76190476

Combine like terms: 6.76190476 + -6.76190476 = 0.00000000
0.00000000 + x = 15.761904761 + -6.76190476
x = 15.761904761 + -6.76190476

Combine like terms: 15.761904761 + -6.76190476 = 9.000000001
x = 9.000000001

Simplifying
x = 9.000000001

Subproblem 2
x + 6.76190476 = -15.761904761

Simplifying
x + 6.76190476 = -15.761904761

Reorder the terms:
6.76190476 + x = -15.761904761

Solving
6.76190476 + x = -15.761904761

Solving for variable 'x'.

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

Add '-6.76190476' to each side of the equation.
6.76190476 + -6.76190476 + x = -15.761904761 + -6.76190476

Combine like terms: 6.76190476 + -6.76190476 = 0.00000000
0.00000000 + x = -15.761904761 + -6.76190476
x = -15.761904761 + -6.76190476

Combine like terms: -15.761904761 + -6.76190476 = -22.523809521
x = -22.523809521

Simplifying
x = -22.523809521

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.000000001, -22.523809521}