17x^2-45x-140=0

Solution for 17x^2-45x-140=0 equation:

Simplifying
17x2 + -45x + -140 = 0

Reorder the terms:
-140 + -45x + 17x2 = 0

Solving
-140 + -45x + 17x2 = 0

Solving for variable 'x'.

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

Divide each side by '17'.
-8.235294118 + -2.647058824x + x2 = 0

Move the constant term to the right:

Add '8.235294118' to each side of the equation.
-8.235294118 + -2.647058824x + 8.235294118 + x2 = 0 + 8.235294118

Reorder the terms:
-8.235294118 + 8.235294118 + -2.647058824x + x2 = 0 + 8.235294118

Combine like terms: -8.235294118 + 8.235294118 = 0.000000000
0.000000000 + -2.647058824x + x2 = 0 + 8.235294118
-2.647058824x + x2 = 0 + 8.235294118

Combine like terms: 0 + 8.235294118 = 8.235294118
-2.647058824x + x2 = 8.235294118

The x term is -2.647058824x.  Take half its coefficient (-1.323529412).
Square it (1.751730104) and add it to both sides.

Add '1.751730104' to each side of the equation.
-2.647058824x + 1.751730104 + x2 = 8.235294118 + 1.751730104

Reorder the terms:
1.751730104 + -2.647058824x + x2 = 8.235294118 + 1.751730104

Combine like terms: 8.235294118 + 1.751730104 = 9.987024222
1.751730104 + -2.647058824x + x2 = 9.987024222

Factor a perfect square on the left side:
(x + -1.323529412)(x + -1.323529412) = 9.987024222

Calculate the square root of the right side: 3.160225344

Break this problem into two subproblems by setting 
(x + -1.323529412) equal to 3.160225344 and -3.160225344.

Subproblem 1
x + -1.323529412 = 3.160225344

Simplifying
x + -1.323529412 = 3.160225344

Reorder the terms:
-1.323529412 + x = 3.160225344

Solving
-1.323529412 + x = 3.160225344

Solving for variable 'x'.

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

Add '1.323529412' to each side of the equation.
-1.323529412 + 1.323529412 + x = 3.160225344 + 1.323529412

Combine like terms: -1.323529412 + 1.323529412 = 0.000000000
0.000000000 + x = 3.160225344 + 1.323529412
x = 3.160225344 + 1.323529412

Combine like terms: 3.160225344 + 1.323529412 = 4.483754756
x = 4.483754756

Simplifying
x = 4.483754756

Subproblem 2
x + -1.323529412 = -3.160225344

Simplifying
x + -1.323529412 = -3.160225344

Reorder the terms:
-1.323529412 + x = -3.160225344

Solving
-1.323529412 + x = -3.160225344

Solving for variable 'x'.

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

Add '1.323529412' to each side of the equation.
-1.323529412 + 1.323529412 + x = -3.160225344 + 1.323529412

Combine like terms: -1.323529412 + 1.323529412 = 0.000000000
0.000000000 + x = -3.160225344 + 1.323529412
x = -3.160225344 + 1.323529412

Combine like terms: -3.160225344 + 1.323529412 = -1.836695932
x = -1.836695932

Simplifying
x = -1.836695932

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.483754756, -1.836695932}