-1.5x^2+4x+3.5=0

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Solution for -1.5x^2+4x+3.5=0 equation:


Simplifying
-1.5x2 + 4x + 3.5 = 0

Reorder the terms:
3.5 + 4x + -1.5x2 = 0

Solving
3.5 + 4x + -1.5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1.5 the coefficient of the squared term: 

Divide each side by '-1.5'.
-2.333333333 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -2.666666667x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -2.666666667x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -2.666666667x + x2 = 0 + 2.333333333
-2.666666667x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-2.666666667x + x2 = 2.333333333

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = 2.333333333 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 2.333333333 + 1.777777780

Combine like terms: 2.333333333 + 1.777777780 = 4.111111113
1.777777780 + -2.666666667x + x2 = 4.111111113

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 4.111111113

Calculate the square root of the right side: 2.027587511

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 2.027587511 and -2.027587511.


Subproblem 1
x + -1.333333334 = 2.027587511

Simplifying
x + -1.333333334 = 2.027587511

Reorder the terms:
-1.333333334 + x = 2.027587511

Solving
-1.333333334 + x = 2.027587511

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 2.027587511 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 2.027587511 + 1.333333334
x = 2.027587511 + 1.333333334

Combine like terms: 2.027587511 + 1.333333334 = 3.360920845
x = 3.360920845

Simplifying
x = 3.360920845


Subproblem 2
x + -1.333333334 = -2.027587511

Simplifying
x + -1.333333334 = -2.027587511

Reorder the terms:
-1.333333334 + x = -2.027587511

Solving
-1.333333334 + x = -2.027587511

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -2.027587511 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -2.027587511 + 1.333333334
x = -2.027587511 + 1.333333334

Combine like terms: -2.027587511 + 1.333333334 = -0.694254177
x = -0.694254177

Simplifying
x = -0.694254177


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.360920845, -0.694254177}

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