-0.9a(a+1)=0.1(a+9)

Solution for -0.9a(a+1)=0.1(a+9) equation:

Simplifying
-0.9a(a + 1) = 0.1(a + 9)

Reorder the terms:
-0.9a(1 + a) = 0.1(a + 9)
(1 * -0.9a + a * -0.9a) = 0.1(a + 9)
(-0.9a + -0.9a2) = 0.1(a + 9)

Reorder the terms:
-0.9a + -0.9a2 = 0.1(9 + a)
-0.9a + -0.9a2 = (9 * 0.1 + a * 0.1)
-0.9a + -0.9a2 = (0.9 + 0.1a)

Solving
-0.9a + -0.9a2 = 0.9 + 0.1a

Solving for variable 'a'.

Reorder the terms:
-0.9 + -0.9a + -0.1a + -0.9a2 = 0.9 + 0.1a + -0.9 + -0.1a

Combine like terms: -0.9a + -0.1a = -1a
-0.9 + -1a + -0.9a2 = 0.9 + 0.1a + -0.9 + -0.1a

Reorder the terms:
-0.9 + -1a + -0.9a2 = 0.9 + -0.9 + 0.1a + -0.1a

Combine like terms: 0.9 + -0.9 = 0.0
-0.9 + -1a + -0.9a2 = 0.0 + 0.1a + -0.1a
-0.9 + -1a + -0.9a2 = 0.1a + -0.1a

Combine like terms: 0.1a + -0.1a = 0.0
-0.9 + -1a + -0.9a2 = 0.0

Begin completing the square.  Divide all terms by
-0.9 the coefficient of the squared term: 

Divide each side by '-0.9'.
1 + 1.111111111a + a2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 1.111111111a + -1 + a2 = 0 + -1

Reorder the terms:
1 + -1 + 1.111111111a + a2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 1.111111111a + a2 = 0 + -1
1.111111111a + a2 = 0 + -1

Combine like terms: 0 + -1 = -1
1.111111111a + a2 = -1

The a term is 1.111111111a.  Take half its coefficient (0.5555555555).
Square it (0.3086419752) and add it to both sides.

Add '0.3086419752' to each side of the equation.
1.111111111a + 0.3086419752 + a2 = -1 + 0.3086419752

Reorder the terms:
0.3086419752 + 1.111111111a + a2 = -1 + 0.3086419752

Combine like terms: -1 + 0.3086419752 = -0.6913580248
0.3086419752 + 1.111111111a + a2 = -0.6913580248

Factor a perfect square on the left side:
(a + 0.5555555555)(a + 0.5555555555) = -0.6913580248

Can't calculate square root of the right side.

The solution to this equation could not be determined.