-15x^2+54x-24=0

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Solution for -15x^2+54x-24=0 equation: 


Simplifying
-15x2 + 54x + -24 = 0

Reorder the terms:
-24 + 54x + -15x2 = 0

Solving
-24 + 54x + -15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 18x + -5x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-8 + 18x + -5x2)' equal to zero and attempt to solve:

Simplifying
-8 + 18x + -5x2 = 0

Solving
-8 + 18x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
1.6 + -3.6x + x2 = 0

Move the constant term to the right:

Add '-1.6' to each side of the equation.
1.6 + -3.6x + -1.6 + x2 = 0 + -1.6

Reorder the terms:
1.6 + -1.6 + -3.6x + x2 = 0 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + -3.6x + x2 = 0 + -1.6
-3.6x + x2 = 0 + -1.6

Combine like terms: 0 + -1.6 = -1.6
-3.6x + x2 = -1.6

The x term is -3.6x.  Take half its coefficient (-1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
-3.6x + 3.24 + x2 = -1.6 + 3.24

Reorder the terms:
3.24 + -3.6x + x2 = -1.6 + 3.24

Combine like terms: -1.6 + 3.24 = 1.64
3.24 + -3.6x + x2 = 1.64

Factor a perfect square on the left side:
(x + -1.8)(x + -1.8) = 1.64

Calculate the square root of the right side: 1.280624847

Break this problem into two subproblems by setting 
(x + -1.8) equal to 1.280624847 and -1.280624847.


Subproblem 1
x + -1.8 = 1.280624847

Simplifying
x + -1.8 = 1.280624847

Reorder the terms:
-1.8 + x = 1.280624847

Solving
-1.8 + x = 1.280624847

Solving for variable 'x'.

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

Add '1.8' to each side of the equation.
-1.8 + 1.8 + x = 1.280624847 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + x = 1.280624847 + 1.8
x = 1.280624847 + 1.8

Combine like terms: 1.280624847 + 1.8 = 3.080624847
x = 3.080624847

Simplifying
x = 3.080624847


Subproblem 2
x + -1.8 = -1.280624847

Simplifying
x + -1.8 = -1.280624847

Reorder the terms:
-1.8 + x = -1.280624847

Solving
-1.8 + x = -1.280624847

Solving for variable 'x'.

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

Add '1.8' to each side of the equation.
-1.8 + 1.8 + x = -1.280624847 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + x = -1.280624847 + 1.8
x = -1.280624847 + 1.8

Combine like terms: -1.280624847 + 1.8 = 0.519375153
x = 0.519375153

Simplifying
x = 0.519375153


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.080624847, 0.519375153}
Solution
x = {3.080624847, 0.519375153}

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