-3x^2+15.9x+1.62=0

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Solution for -3x^2+15.9x+1.62=0 equation: 


Simplifying
-3x2 + 15.9x + 1.62 = 0

Reorder the terms:
1.62 + 15.9x + -3x2 = 0

Solving
1.62 + 15.9x + -3x2 = 0

Solving for variable 'x'.

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

Divide each side by '-3'.
-0.54 + -5.3x + x2 = 0

Move the constant term to the right:

Add '0.54' to each side of the equation.
-0.54 + -5.3x + 0.54 + x2 = 0 + 0.54

Reorder the terms:
-0.54 + 0.54 + -5.3x + x2 = 0 + 0.54

Combine like terms: -0.54 + 0.54 = 0.00
0.00 + -5.3x + x2 = 0 + 0.54
-5.3x + x2 = 0 + 0.54

Combine like terms: 0 + 0.54 = 0.54
-5.3x + x2 = 0.54

The x term is -5.3x.  Take half its coefficient (-2.65).
Square it (7.0225) and add it to both sides.

Add '7.0225' to each side of the equation.
-5.3x + 7.0225 + x2 = 0.54 + 7.0225

Reorder the terms:
7.0225 + -5.3x + x2 = 0.54 + 7.0225

Combine like terms: 0.54 + 7.0225 = 7.5625
7.0225 + -5.3x + x2 = 7.5625

Factor a perfect square on the left side:
(x + -2.65)(x + -2.65) = 7.5625

Calculate the square root of the right side: 2.75

Break this problem into two subproblems by setting 
(x + -2.65) equal to 2.75 and -2.75.


Subproblem 1
x + -2.65 = 2.75

Simplifying
x + -2.65 = 2.75

Reorder the terms:
-2.65 + x = 2.75

Solving
-2.65 + x = 2.75

Solving for variable 'x'.

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

Add '2.65' to each side of the equation.
-2.65 + 2.65 + x = 2.75 + 2.65

Combine like terms: -2.65 + 2.65 = 0.00
0.00 + x = 2.75 + 2.65
x = 2.75 + 2.65

Combine like terms: 2.75 + 2.65 = 5.4
x = 5.4

Simplifying
x = 5.4


Subproblem 2
x + -2.65 = -2.75

Simplifying
x + -2.65 = -2.75

Reorder the terms:
-2.65 + x = -2.75

Solving
-2.65 + x = -2.75

Solving for variable 'x'.

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

Add '2.65' to each side of the equation.
-2.65 + 2.65 + x = -2.75 + 2.65

Combine like terms: -2.65 + 2.65 = 0.00
0.00 + x = -2.75 + 2.65
x = -2.75 + 2.65

Combine like terms: -2.75 + 2.65 = -0.1
x = -0.1

Simplifying
x = -0.1


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.4, -0.1}

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