0.75x^2+1.5x-4=0

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Solution for 0.75x^2+1.5x-4=0 equation: 


Simplifying
0.75x2 + 1.5x + -4 = 0

Reorder the terms:
-4 + 1.5x + 0.75x2 = 0

Solving
-4 + 1.5x + 0.75x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.75'.
-5.333333333 + 2x + x2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + 2x + 5.333333333 + x2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + 2x + x2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + 2x + x2 = 0 + 5.333333333
2x + x2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
2x + x2 = 5.333333333

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 5.333333333 + 1

Reorder the terms:
1 + 2x + x2 = 5.333333333 + 1

Combine like terms: 5.333333333 + 1 = 6.333333333
1 + 2x + x2 = 6.333333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 6.333333333

Calculate the square root of the right side: 2.516611478

Break this problem into two subproblems by setting 
(x + 1) equal to 2.516611478 and -2.516611478.


Subproblem 1
x + 1 = 2.516611478

Simplifying
x + 1 = 2.516611478

Reorder the terms:
1 + x = 2.516611478

Solving
1 + x = 2.516611478

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 2.516611478 + -1

Combine like terms: 1 + -1 = 0
0 + x = 2.516611478 + -1
x = 2.516611478 + -1

Combine like terms: 2.516611478 + -1 = 1.516611478
x = 1.516611478

Simplifying
x = 1.516611478


Subproblem 2
x + 1 = -2.516611478

Simplifying
x + 1 = -2.516611478

Reorder the terms:
1 + x = -2.516611478

Solving
1 + x = -2.516611478

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -2.516611478 + -1

Combine like terms: 1 + -1 = 0
0 + x = -2.516611478 + -1
x = -2.516611478 + -1

Combine like terms: -2.516611478 + -1 = -3.516611478
x = -3.516611478

Simplifying
x = -3.516611478


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.516611478, -3.516611478}

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