4x^2+98x-336=0

Solution for 4x^2+98x-336=0 equation:

Simplifying
4x2 + 98x + -336 = 0

Reorder the terms:
-336 + 98x + 4x2 = 0

Solving
-336 + 98x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-168 + 49x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-168 + 49x + 2x2)' equal to zero and attempt to solve:

Simplifying
-168 + 49x + 2x2 = 0

Solving
-168 + 49x + 2x2 = 0

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

Divide each side by '2'.
-84 + 24.5x + x2 = 0

Move the constant term to the right:

Add '84' to each side of the equation.
-84 + 24.5x + 84 + x2 = 0 + 84

Reorder the terms:
-84 + 84 + 24.5x + x2 = 0 + 84

Combine like terms: -84 + 84 = 0
0 + 24.5x + x2 = 0 + 84
24.5x + x2 = 0 + 84

Combine like terms: 0 + 84 = 84
24.5x + x2 = 84

The x term is 24.5x.  Take half its coefficient (12.25).
Square it (150.0625) and add it to both sides.

Add '150.0625' to each side of the equation.
24.5x + 150.0625 + x2 = 84 + 150.0625

Reorder the terms:
150.0625 + 24.5x + x2 = 84 + 150.0625

Combine like terms: 84 + 150.0625 = 234.0625
150.0625 + 24.5x + x2 = 234.0625

Factor a perfect square on the left side:
(x + 12.25)(x + 12.25) = 234.0625

Calculate the square root of the right side: 15.299101281

Break this problem into two subproblems by setting 
(x + 12.25) equal to 15.299101281 and -15.299101281.

Subproblem 1
x + 12.25 = 15.299101281

Simplifying
x + 12.25 = 15.299101281

Reorder the terms:
12.25 + x = 15.299101281

Solving
12.25 + x = 15.299101281

Solving for variable 'x'.

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

Add '-12.25' to each side of the equation.
12.25 + -12.25 + x = 15.299101281 + -12.25

Combine like terms: 12.25 + -12.25 = 0.00
0.00 + x = 15.299101281 + -12.25
x = 15.299101281 + -12.25

Combine like terms: 15.299101281 + -12.25 = 3.049101281
x = 3.049101281

Simplifying
x = 3.049101281

Subproblem 2
x + 12.25 = -15.299101281

Simplifying
x + 12.25 = -15.299101281

Reorder the terms:
12.25 + x = -15.299101281

Solving
12.25 + x = -15.299101281

Solving for variable 'x'.

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

Add '-12.25' to each side of the equation.
12.25 + -12.25 + x = -15.299101281 + -12.25

Combine like terms: 12.25 + -12.25 = 0.00
0.00 + x = -15.299101281 + -12.25
x = -15.299101281 + -12.25

Combine like terms: -15.299101281 + -12.25 = -27.549101281
x = -27.549101281

Simplifying
x = -27.549101281

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.049101281, -27.549101281}
Solution
x = {3.049101281, -27.549101281}