9s^2=10s-1

Solution for 9s^2=10s-1 equation:

Simplifying
9s2 = 10s + -1

Reorder the terms:
9s2 = -1 + 10s

Solving
9s2 = -1 + 10s

Solving for variable 's'.

Reorder the terms:
1 + -10s + 9s2 = -1 + 10s + 1 + -10s

Reorder the terms:
1 + -10s + 9s2 = -1 + 1 + 10s + -10s

Combine like terms: -1 + 1 = 0
1 + -10s + 9s2 = 0 + 10s + -10s
1 + -10s + 9s2 = 10s + -10s

Combine like terms: 10s + -10s = 0
1 + -10s + 9s2 = 0

Factor a trinomial.
(1 + -9s)(1 + -1s) = 0

Subproblem 1
Set the factor '(1 + -9s)' equal to zero and attempt to solve:

Simplifying
1 + -9s = 0

Solving
1 + -9s = 0

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

Add '-1' to each side of the equation.
1 + -1 + -9s = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -9s = 0 + -1
-9s = 0 + -1

Combine like terms: 0 + -1 = -1
-9s = -1

Divide each side by '-9'.
s = 0.1111111111

Simplifying
s = 0.1111111111
Subproblem 2
Set the factor '(1 + -1s)' equal to zero and attempt to solve:

Simplifying
1 + -1s = 0

Solving
1 + -1s = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1s = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1s = 0 + -1
-1s = 0 + -1

Combine like terms: 0 + -1 = -1
-1s = -1

Divide each side by '-1'.
s = 1

Simplifying
s = 1
Solution
s = {0.1111111111, 1}