15x^2-8x-3=0

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Solution for 15x^2-8x-3=0 equation: 


Simplifying
15x2 + -8x + -3 = 0

Reorder the terms:
-3 + -8x + 15x2 = 0

Solving
-3 + -8x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
-0.2 + -0.5333333333x + x2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -0.5333333333x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -0.5333333333x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -0.5333333333x + x2 = 0 + 0.2
-0.5333333333x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-0.5333333333x + x2 = 0.2

The x term is -0.5333333333x.  Take half its coefficient (-0.2666666667).
Square it (0.07111111113) and add it to both sides.

Add '0.07111111113' to each side of the equation.
-0.5333333333x + 0.07111111113 + x2 = 0.2 + 0.07111111113

Reorder the terms:
0.07111111113 + -0.5333333333x + x2 = 0.2 + 0.07111111113

Combine like terms: 0.2 + 0.07111111113 = 0.27111111113
0.07111111113 + -0.5333333333x + x2 = 0.27111111113

Factor a perfect square on the left side:
(x + -0.2666666667)(x + -0.2666666667) = 0.27111111113

Calculate the square root of the right side: 0.520683312

Break this problem into two subproblems by setting 
(x + -0.2666666667) equal to 0.520683312 and -0.520683312.


Subproblem 1
x + -0.2666666667 = 0.520683312

Simplifying
x + -0.2666666667 = 0.520683312

Reorder the terms:
-0.2666666667 + x = 0.520683312

Solving
-0.2666666667 + x = 0.520683312

Solving for variable 'x'.

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

Add '0.2666666667' to each side of the equation.
-0.2666666667 + 0.2666666667 + x = 0.520683312 + 0.2666666667

Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000
0.0000000000 + x = 0.520683312 + 0.2666666667
x = 0.520683312 + 0.2666666667

Combine like terms: 0.520683312 + 0.2666666667 = 0.7873499787
x = 0.7873499787

Simplifying
x = 0.7873499787


Subproblem 2
x + -0.2666666667 = -0.520683312

Simplifying
x + -0.2666666667 = -0.520683312

Reorder the terms:
-0.2666666667 + x = -0.520683312

Solving
-0.2666666667 + x = -0.520683312

Solving for variable 'x'.

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

Add '0.2666666667' to each side of the equation.
-0.2666666667 + 0.2666666667 + x = -0.520683312 + 0.2666666667

Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000
0.0000000000 + x = -0.520683312 + 0.2666666667
x = -0.520683312 + 0.2666666667

Combine like terms: -0.520683312 + 0.2666666667 = -0.2540166453
x = -0.2540166453

Simplifying
x = -0.2540166453


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7873499787, -0.2540166453}

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