90r^2-5r-10=0

Solution for 90r^2-5r-10=0 equation:

Simplifying
90r2 + -5r + -10 = 0

Reorder the terms:
-10 + -5r + 90r2 = 0

Solving
-10 + -5r + 90r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + -1r + 18r2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-2 + -1r + 18r2)' equal to zero and attempt to solve:

Simplifying
-2 + -1r + 18r2 = 0

Solving
-2 + -1r + 18r2 = 0

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

Divide each side by '18'.
-0.1111111111 + -0.05555555556r + r2 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + -0.05555555556r + 0.1111111111 + r2 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + -0.05555555556r + r2 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + -0.05555555556r + r2 = 0 + 0.1111111111
-0.05555555556r + r2 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
-0.05555555556r + r2 = 0.1111111111

The r term is -0.05555555556r.  Take half its coefficient (-0.02777777778).
Square it (0.0007716049384) and add it to both sides.

Add '0.0007716049384' to each side of the equation.
-0.05555555556r + 0.0007716049384 + r2 = 0.1111111111 + 0.0007716049384

Reorder the terms:
0.0007716049384 + -0.05555555556r + r2 = 0.1111111111 + 0.0007716049384

Combine like terms: 0.1111111111 + 0.0007716049384 = 0.1118827160384
0.0007716049384 + -0.05555555556r + r2 = 0.1118827160384

Factor a perfect square on the left side:
(r + -0.02777777778)(r + -0.02777777778) = 0.1118827160384

Calculate the square root of the right side: 0.334488738

Break this problem into two subproblems by setting 
(r + -0.02777777778) equal to 0.334488738 and -0.334488738.

Subproblem 1
r + -0.02777777778 = 0.334488738

Simplifying
r + -0.02777777778 = 0.334488738

Reorder the terms:
-0.02777777778 + r = 0.334488738

Solving
-0.02777777778 + r = 0.334488738

Solving for variable 'r'.

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

Add '0.02777777778' to each side of the equation.
-0.02777777778 + 0.02777777778 + r = 0.334488738 + 0.02777777778

Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000
0.00000000000 + r = 0.334488738 + 0.02777777778
r = 0.334488738 + 0.02777777778

Combine like terms: 0.334488738 + 0.02777777778 = 0.36226651578
r = 0.36226651578

Simplifying
r = 0.36226651578

Subproblem 2
r + -0.02777777778 = -0.334488738

Simplifying
r + -0.02777777778 = -0.334488738

Reorder the terms:
-0.02777777778 + r = -0.334488738

Solving
-0.02777777778 + r = -0.334488738

Solving for variable 'r'.

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

Add '0.02777777778' to each side of the equation.
-0.02777777778 + 0.02777777778 + r = -0.334488738 + 0.02777777778

Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000
0.00000000000 + r = -0.334488738 + 0.02777777778
r = -0.334488738 + 0.02777777778

Combine like terms: -0.334488738 + 0.02777777778 = -0.30671096022
r = -0.30671096022

Simplifying
r = -0.30671096022

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.36226651578, -0.30671096022}
Solution
r = {0.36226651578, -0.30671096022}