0.3x^2+2.4x-1.9=0

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Solution for 0.3x^2+2.4x-1.9=0 equation: 


Simplifying
0.3x2 + 2.4x + -1.9 = 0

Reorder the terms:
-1.9 + 2.4x + 0.3x2 = 0

Solving
-1.9 + 2.4x + 0.3x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.3'.
-6.333333333 + 8x + x2 = 0

Move the constant term to the right:

Add '6.333333333' to each side of the equation.
-6.333333333 + 8x + 6.333333333 + x2 = 0 + 6.333333333

Reorder the terms:
-6.333333333 + 6.333333333 + 8x + x2 = 0 + 6.333333333

Combine like terms: -6.333333333 + 6.333333333 = 0.000000000
0.000000000 + 8x + x2 = 0 + 6.333333333
8x + x2 = 0 + 6.333333333

Combine like terms: 0 + 6.333333333 = 6.333333333
8x + x2 = 6.333333333

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 6.333333333 + 16

Reorder the terms:
16 + 8x + x2 = 6.333333333 + 16

Combine like terms: 6.333333333 + 16 = 22.333333333
16 + 8x + x2 = 22.333333333

Factor a perfect square on the left side:
(x + 4)(x + 4) = 22.333333333

Calculate the square root of the right side: 4.725815626

Break this problem into two subproblems by setting 
(x + 4) equal to 4.725815626 and -4.725815626.


Subproblem 1
x + 4 = 4.725815626

Simplifying
x + 4 = 4.725815626

Reorder the terms:
4 + x = 4.725815626

Solving
4 + x = 4.725815626

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 4.725815626 + -4

Combine like terms: 4 + -4 = 0
0 + x = 4.725815626 + -4
x = 4.725815626 + -4

Combine like terms: 4.725815626 + -4 = 0.725815626
x = 0.725815626

Simplifying
x = 0.725815626


Subproblem 2
x + 4 = -4.725815626

Simplifying
x + 4 = -4.725815626

Reorder the terms:
4 + x = -4.725815626

Solving
4 + x = -4.725815626

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -4.725815626 + -4

Combine like terms: 4 + -4 = 0
0 + x = -4.725815626 + -4
x = -4.725815626 + -4

Combine like terms: -4.725815626 + -4 = -8.725815626
x = -8.725815626

Simplifying
x = -8.725815626


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.725815626, -8.725815626}

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