147x^2+14x-70=91x^2-450x

Solution for 147x^2+14x-70=91x^2-450x equation:

Simplifying
147x2 + 14x + -70 = 91x2 + -450x

Reorder the terms:
-70 + 14x + 147x2 = 91x2 + -450x

Reorder the terms:
-70 + 14x + 147x2 = -450x + 91x2

Solving
-70 + 14x + 147x2 = -450x + 91x2

Solving for variable 'x'.

Reorder the terms:
-70 + 14x + 450x + 147x2 + -91x2 = -450x + 91x2 + 450x + -91x2

Combine like terms: 14x + 450x = 464x
-70 + 464x + 147x2 + -91x2 = -450x + 91x2 + 450x + -91x2

Combine like terms: 147x2 + -91x2 = 56x2
-70 + 464x + 56x2 = -450x + 91x2 + 450x + -91x2

Reorder the terms:
-70 + 464x + 56x2 = -450x + 450x + 91x2 + -91x2

Combine like terms: -450x + 450x = 0
-70 + 464x + 56x2 = 0 + 91x2 + -91x2
-70 + 464x + 56x2 = 91x2 + -91x2

Combine like terms: 91x2 + -91x2 = 0
-70 + 464x + 56x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + 232x + 28x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-35 + 232x + 28x2)' equal to zero and attempt to solve:

Simplifying
-35 + 232x + 28x2 = 0

Solving
-35 + 232x + 28x2 = 0

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

Divide each side by '28'.
-1.25 + 8.285714286x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 8.285714286x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 8.285714286x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 8.285714286x + x2 = 0 + 1.25
8.285714286x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
8.285714286x + x2 = 1.25

The x term is 8.285714286x.  Take half its coefficient (4.142857143).
Square it (17.16326531) and add it to both sides.

Add '17.16326531' to each side of the equation.
8.285714286x + 17.16326531 + x2 = 1.25 + 17.16326531

Reorder the terms:
17.16326531 + 8.285714286x + x2 = 1.25 + 17.16326531

Combine like terms: 1.25 + 17.16326531 = 18.41326531
17.16326531 + 8.285714286x + x2 = 18.41326531

Factor a perfect square on the left side:
(x + 4.142857143)(x + 4.142857143) = 18.41326531

Calculate the square root of the right side: 4.291068085

Break this problem into two subproblems by setting 
(x + 4.142857143) equal to 4.291068085 and -4.291068085.

Subproblem 1
x + 4.142857143 = 4.291068085

Simplifying
x + 4.142857143 = 4.291068085

Reorder the terms:
4.142857143 + x = 4.291068085

Solving
4.142857143 + x = 4.291068085

Solving for variable 'x'.

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

Add '-4.142857143' to each side of the equation.
4.142857143 + -4.142857143 + x = 4.291068085 + -4.142857143

Combine like terms: 4.142857143 + -4.142857143 = 0.000000000
0.000000000 + x = 4.291068085 + -4.142857143
x = 4.291068085 + -4.142857143

Combine like terms: 4.291068085 + -4.142857143 = 0.148210942
x = 0.148210942

Simplifying
x = 0.148210942

Subproblem 2
x + 4.142857143 = -4.291068085

Simplifying
x + 4.142857143 = -4.291068085

Reorder the terms:
4.142857143 + x = -4.291068085

Solving
4.142857143 + x = -4.291068085

Solving for variable 'x'.

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

Add '-4.142857143' to each side of the equation.
4.142857143 + -4.142857143 + x = -4.291068085 + -4.142857143

Combine like terms: 4.142857143 + -4.142857143 = 0.000000000
0.000000000 + x = -4.291068085 + -4.142857143
x = -4.291068085 + -4.142857143

Combine like terms: -4.291068085 + -4.142857143 = -8.433925228
x = -8.433925228

Simplifying
x = -8.433925228

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.148210942, -8.433925228}
Solution
x = {0.148210942, -8.433925228}