14x^2y+17xy-24y=

Solution for 14x^2y+17xy-24y= equation:

Simplifying
14x2y + 17xy + -24y = 0

Reorder the terms:
17xy + 14x2y + -24y = 0

Solving
17xy + 14x2y + -24y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(17x + 14x2 + -24) = 0

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(17x + 14x2 + -24)' equal to zero and attempt to solve:

Simplifying
17x + 14x2 + -24 = 0

Reorder the terms:
-24 + 17x + 14x2 = 0

Solving
-24 + 17x + 14x2 = 0

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

Divide each side by '14'.
-1.714285714 + 1.214285714x + x2 = 0

Move the constant term to the right:

Add '1.714285714' to each side of the equation.
-1.714285714 + 1.214285714x + 1.714285714 + x2 = 0 + 1.714285714

Reorder the terms:
-1.714285714 + 1.714285714 + 1.214285714x + x2 = 0 + 1.714285714

Combine like terms: -1.714285714 + 1.714285714 = 0.000000000
0.000000000 + 1.214285714x + x2 = 0 + 1.714285714
1.214285714x + x2 = 0 + 1.714285714

Combine like terms: 0 + 1.714285714 = 1.714285714
1.214285714x + x2 = 1.714285714

The x term is 1.214285714x.  Take half its coefficient (0.607142857).
Square it (0.3686224488) and add it to both sides.

Add '0.3686224488' to each side of the equation.
1.214285714x + 0.3686224488 + x2 = 1.714285714 + 0.3686224488

Reorder the terms:
0.3686224488 + 1.214285714x + x2 = 1.714285714 + 0.3686224488

Combine like terms: 1.714285714 + 0.3686224488 = 2.0829081628
0.3686224488 + 1.214285714x + x2 = 2.0829081628

Factor a perfect square on the left side:
(x + 0.607142857)(x + 0.607142857) = 2.0829081628

Calculate the square root of the right side: 1.443228382

Break this problem into two subproblems by setting 
(x + 0.607142857) equal to 1.443228382 and -1.443228382.

Subproblem 1
x + 0.607142857 = 1.443228382

Simplifying
x + 0.607142857 = 1.443228382

Reorder the terms:
0.607142857 + x = 1.443228382

Solving
0.607142857 + x = 1.443228382

Solving for variable 'x'.

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

Add '-0.607142857' to each side of the equation.
0.607142857 + -0.607142857 + x = 1.443228382 + -0.607142857

Combine like terms: 0.607142857 + -0.607142857 = 0.000000000
0.000000000 + x = 1.443228382 + -0.607142857
x = 1.443228382 + -0.607142857

Combine like terms: 1.443228382 + -0.607142857 = 0.836085525
x = 0.836085525

Simplifying
x = 0.836085525

Subproblem 2
x + 0.607142857 = -1.443228382

Simplifying
x + 0.607142857 = -1.443228382

Reorder the terms:
0.607142857 + x = -1.443228382

Solving
0.607142857 + x = -1.443228382

Solving for variable 'x'.

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

Add '-0.607142857' to each side of the equation.
0.607142857 + -0.607142857 + x = -1.443228382 + -0.607142857

Combine like terms: 0.607142857 + -0.607142857 = 0.000000000
0.000000000 + x = -1.443228382 + -0.607142857
x = -1.443228382 + -0.607142857

Combine like terms: -1.443228382 + -0.607142857 = -2.050371239
x = -2.050371239

Simplifying
x = -2.050371239

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.836085525, -2.050371239}
Solution
x = {0.836085525, -2.050371239}