3x^2-26x=4x^2-9x-6

Solution for 3x^2-26x=4x^2-9x-6 equation:

Simplifying
3x2 + -26x = 4x2 + -9x + -6

Reorder the terms:
-26x + 3x2 = 4x2 + -9x + -6

Reorder the terms:
-26x + 3x2 = -6 + -9x + 4x2

Solving
-26x + 3x2 = -6 + -9x + 4x2

Solving for variable 'x'.

Reorder the terms:
6 + -26x + 9x + 3x2 + -4x2 = -6 + -9x + 4x2 + 6 + 9x + -4x2

Combine like terms: -26x + 9x = -17x
6 + -17x + 3x2 + -4x2 = -6 + -9x + 4x2 + 6 + 9x + -4x2

Combine like terms: 3x2 + -4x2 = -1x2
6 + -17x + -1x2 = -6 + -9x + 4x2 + 6 + 9x + -4x2

Reorder the terms:
6 + -17x + -1x2 = -6 + 6 + -9x + 9x + 4x2 + -4x2

Combine like terms: -6 + 6 = 0
6 + -17x + -1x2 = 0 + -9x + 9x + 4x2 + -4x2
6 + -17x + -1x2 = -9x + 9x + 4x2 + -4x2

Combine like terms: -9x + 9x = 0
6 + -17x + -1x2 = 0 + 4x2 + -4x2
6 + -17x + -1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
6 + -17x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + 17x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 17x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 17x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 17x + x2 = 0 + 6
17x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
17x + x2 = 6

The x term is 17x.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17x + 72.25 + x2 = 6 + 72.25

Reorder the terms:
72.25 + 17x + x2 = 6 + 72.25

Combine like terms: 6 + 72.25 = 78.25
72.25 + 17x + x2 = 78.25

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 78.25

Calculate the square root of the right side: 8.845903006

Break this problem into two subproblems by setting 
(x + 8.5) equal to 8.845903006 and -8.845903006.

Subproblem 1
x + 8.5 = 8.845903006

Simplifying
x + 8.5 = 8.845903006

Reorder the terms:
8.5 + x = 8.845903006

Solving
8.5 + x = 8.845903006

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = 8.845903006 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = 8.845903006 + -8.5
x = 8.845903006 + -8.5

Combine like terms: 8.845903006 + -8.5 = 0.345903006
x = 0.345903006

Simplifying
x = 0.345903006

Subproblem 2
x + 8.5 = -8.845903006

Simplifying
x + 8.5 = -8.845903006

Reorder the terms:
8.5 + x = -8.845903006

Solving
8.5 + x = -8.845903006

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = -8.845903006 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = -8.845903006 + -8.5
x = -8.845903006 + -8.5

Combine like terms: -8.845903006 + -8.5 = -17.345903006
x = -17.345903006

Simplifying
x = -17.345903006

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.345903006, -17.345903006}