98x^2=8x+108

Solution for 98x^2=8x+108 equation:

Simplifying
98x2 = 8x + 108

Reorder the terms:
98x2 = 108 + 8x

Solving
98x2 = 108 + 8x

Solving for variable 'x'.

Reorder the terms:
-108 + -8x + 98x2 = 108 + 8x + -108 + -8x

Reorder the terms:
-108 + -8x + 98x2 = 108 + -108 + 8x + -8x

Combine like terms: 108 + -108 = 0
-108 + -8x + 98x2 = 0 + 8x + -8x
-108 + -8x + 98x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-108 + -8x + 98x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-54 + -4x + 49x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-54 + -4x + 49x2)' equal to zero and attempt to solve:

Simplifying
-54 + -4x + 49x2 = 0

Solving
-54 + -4x + 49x2 = 0

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

Divide each side by '49'.
-1.102040816 + -0.08163265306x + x2 = 0

Move the constant term to the right:

Add '1.102040816' to each side of the equation.
-1.102040816 + -0.08163265306x + 1.102040816 + x2 = 0 + 1.102040816

Reorder the terms:
-1.102040816 + 1.102040816 + -0.08163265306x + x2 = 0 + 1.102040816

Combine like terms: -1.102040816 + 1.102040816 = 0.000000000
0.000000000 + -0.08163265306x + x2 = 0 + 1.102040816
-0.08163265306x + x2 = 0 + 1.102040816

Combine like terms: 0 + 1.102040816 = 1.102040816
-0.08163265306x + x2 = 1.102040816

The x term is -0.08163265306x.  Take half its coefficient (-0.04081632653).
Square it (0.001665972511) and add it to both sides.

Add '0.001665972511' to each side of the equation.
-0.08163265306x + 0.001665972511 + x2 = 1.102040816 + 0.001665972511

Reorder the terms:
0.001665972511 + -0.08163265306x + x2 = 1.102040816 + 0.001665972511

Combine like terms: 1.102040816 + 0.001665972511 = 1.103706788511
0.001665972511 + -0.08163265306x + x2 = 1.103706788511

Factor a perfect square on the left side:
(x + -0.04081632653)(x + -0.04081632653) = 1.103706788511

Calculate the square root of the right side: 1.050574504

Break this problem into two subproblems by setting 
(x + -0.04081632653) equal to 1.050574504 and -1.050574504.

Subproblem 1
x + -0.04081632653 = 1.050574504

Simplifying
x + -0.04081632653 = 1.050574504

Reorder the terms:
-0.04081632653 + x = 1.050574504

Solving
-0.04081632653 + x = 1.050574504

Solving for variable 'x'.

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

Add '0.04081632653' to each side of the equation.
-0.04081632653 + 0.04081632653 + x = 1.050574504 + 0.04081632653

Combine like terms: -0.04081632653 + 0.04081632653 = 0.00000000000
0.00000000000 + x = 1.050574504 + 0.04081632653
x = 1.050574504 + 0.04081632653

Combine like terms: 1.050574504 + 0.04081632653 = 1.09139083053
x = 1.09139083053

Simplifying
x = 1.09139083053

Subproblem 2
x + -0.04081632653 = -1.050574504

Simplifying
x + -0.04081632653 = -1.050574504

Reorder the terms:
-0.04081632653 + x = -1.050574504

Solving
-0.04081632653 + x = -1.050574504

Solving for variable 'x'.

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

Add '0.04081632653' to each side of the equation.
-0.04081632653 + 0.04081632653 + x = -1.050574504 + 0.04081632653

Combine like terms: -0.04081632653 + 0.04081632653 = 0.00000000000
0.00000000000 + x = -1.050574504 + 0.04081632653
x = -1.050574504 + 0.04081632653

Combine like terms: -1.050574504 + 0.04081632653 = -1.00975817747
x = -1.00975817747

Simplifying
x = -1.00975817747

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.09139083053, -1.00975817747}
Solution
x = {1.09139083053, -1.00975817747}