2+0.8x=0.25x^2-1.5x

Solution for 2+0.8x=0.25x^2-1.5x equation:

Simplifying
2 + 0.8x = 0.25x2 + -1.5x

Reorder the terms:
2 + 0.8x = -1.5x + 0.25x2

Solving
2 + 0.8x = -1.5x + 0.25x2

Solving for variable 'x'.

Combine like terms: 0.8x + 1.5x = 2.3x
2 + 2.3x + -0.25x2 = -1.5x + 0.25x2 + 1.5x + -0.25x2

Reorder the terms:
2 + 2.3x + -0.25x2 = -1.5x + 1.5x + 0.25x2 + -0.25x2

Combine like terms: -1.5x + 1.5x = 0.0
2 + 2.3x + -0.25x2 = 0.0 + 0.25x2 + -0.25x2
2 + 2.3x + -0.25x2 = 0.25x2 + -0.25x2

Combine like terms: 0.25x2 + -0.25x2 = 0.00
2 + 2.3x + -0.25x2 = 0.00

Begin completing the square.  Divide all terms by
-0.25 the coefficient of the squared term: 

Divide each side by '-0.25'.
-8 + -9.2x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -9.2x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -9.2x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -9.2x + x2 = 0 + 8
-9.2x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-9.2x + x2 = 8

The x term is -9.2x.  Take half its coefficient (-4.6).
Square it (21.16) and add it to both sides.

Add '21.16' to each side of the equation.
-9.2x + 21.16 + x2 = 8 + 21.16

Reorder the terms:
21.16 + -9.2x + x2 = 8 + 21.16

Combine like terms: 8 + 21.16 = 29.16
21.16 + -9.2x + x2 = 29.16

Factor a perfect square on the left side:
(x + -4.6)(x + -4.6) = 29.16

Calculate the square root of the right side: 5.4

Break this problem into two subproblems by setting 
(x + -4.6) equal to 5.4 and -5.4.

Subproblem 1
x + -4.6 = 5.4

Simplifying
x + -4.6 = 5.4

Reorder the terms:
-4.6 + x = 5.4

Solving
-4.6 + x = 5.4

Solving for variable 'x'.

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

Add '4.6' to each side of the equation.
-4.6 + 4.6 + x = 5.4 + 4.6

Combine like terms: -4.6 + 4.6 = 0.0
0.0 + x = 5.4 + 4.6
x = 5.4 + 4.6

Combine like terms: 5.4 + 4.6 = 10
x = 10

Simplifying
x = 10

Subproblem 2
x + -4.6 = -5.4

Simplifying
x + -4.6 = -5.4

Reorder the terms:
-4.6 + x = -5.4

Solving
-4.6 + x = -5.4

Solving for variable 'x'.

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

Add '4.6' to each side of the equation.
-4.6 + 4.6 + x = -5.4 + 4.6

Combine like terms: -4.6 + 4.6 = 0.0
0.0 + x = -5.4 + 4.6
x = -5.4 + 4.6

Combine like terms: -5.4 + 4.6 = -0.8
x = -0.8

Simplifying
x = -0.8

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10, -0.8}