-15x^2+85x-27=0

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Solution for -15x^2+85x-27=0 equation: 


Simplifying
-15x2 + 85x + -27 = 0

Reorder the terms:
-27 + 85x + -15x2 = 0

Solving
-27 + 85x + -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'.
1.8 + -5.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.8' to each side of the equation.
1.8 + -5.666666667x + -1.8 + x2 = 0 + -1.8

Reorder the terms:
1.8 + -1.8 + -5.666666667x + x2 = 0 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + -5.666666667x + x2 = 0 + -1.8
-5.666666667x + x2 = 0 + -1.8

Combine like terms: 0 + -1.8 = -1.8
-5.666666667x + x2 = -1.8

The x term is -5.666666667x.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667x + 8.027777782 + x2 = -1.8 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667x + x2 = -1.8 + 8.027777782

Combine like terms: -1.8 + 8.027777782 = 6.227777782
8.027777782 + -5.666666667x + x2 = 6.227777782

Factor a perfect square on the left side:
(x + -2.833333334)(x + -2.833333334) = 6.227777782

Calculate the square root of the right side: 2.495551599

Break this problem into two subproblems by setting 
(x + -2.833333334) equal to 2.495551599 and -2.495551599.


Subproblem 1
x + -2.833333334 = 2.495551599

Simplifying
x + -2.833333334 = 2.495551599

Reorder the terms:
-2.833333334 + x = 2.495551599

Solving
-2.833333334 + x = 2.495551599

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = 2.495551599 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = 2.495551599 + 2.833333334
x = 2.495551599 + 2.833333334

Combine like terms: 2.495551599 + 2.833333334 = 5.328884933
x = 5.328884933

Simplifying
x = 5.328884933


Subproblem 2
x + -2.833333334 = -2.495551599

Simplifying
x + -2.833333334 = -2.495551599

Reorder the terms:
-2.833333334 + x = -2.495551599

Solving
-2.833333334 + x = -2.495551599

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = -2.495551599 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = -2.495551599 + 2.833333334
x = -2.495551599 + 2.833333334

Combine like terms: -2.495551599 + 2.833333334 = 0.337781735
x = 0.337781735

Simplifying
x = 0.337781735


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.328884933, 0.337781735}

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