6x^2+10x-102=0

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Solution for 6x^2+10x-102=0 equation: 


Simplifying
6x2 + 10x + -102 = 0

Reorder the terms:
-102 + 10x + 6x2 = 0

Solving
-102 + 10x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-51 + 5x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-51 + 5x + 3x2)' equal to zero and attempt to solve:

Simplifying
-51 + 5x + 3x2 = 0

Solving
-51 + 5x + 3x2 = 0

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

Divide each side by '3'.
-17 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 1.666666667x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + 1.666666667x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 1.666666667x + x2 = 0 + 17
1.666666667x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
1.666666667x + x2 = 17

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 17 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 17 + 0.6944444447

Combine like terms: 17 + 0.6944444447 = 17.6944444447
0.6944444447 + 1.666666667x + x2 = 17.6944444447

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 17.6944444447

Calculate the square root of the right side: 4.206476488

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 4.206476488 and -4.206476488.


Subproblem 1
x + 0.8333333335 = 4.206476488

Simplifying
x + 0.8333333335 = 4.206476488

Reorder the terms:
0.8333333335 + x = 4.206476488

Solving
0.8333333335 + x = 4.206476488

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 4.206476488 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 4.206476488 + -0.8333333335
x = 4.206476488 + -0.8333333335

Combine like terms: 4.206476488 + -0.8333333335 = 3.3731431545
x = 3.3731431545

Simplifying
x = 3.3731431545


Subproblem 2
x + 0.8333333335 = -4.206476488

Simplifying
x + 0.8333333335 = -4.206476488

Reorder the terms:
0.8333333335 + x = -4.206476488

Solving
0.8333333335 + x = -4.206476488

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -4.206476488 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -4.206476488 + -0.8333333335
x = -4.206476488 + -0.8333333335

Combine like terms: -4.206476488 + -0.8333333335 = -5.0398098215
x = -5.0398098215

Simplifying
x = -5.0398098215


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.3731431545, -5.0398098215}
Solution
x = {3.3731431545, -5.0398098215}

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