8v^2-22v+9=0

Solution for 8v^2-22v+9=0 equation:

Simplifying
8v2 + -22v + 9 = 0

Reorder the terms:
9 + -22v + 8v2 = 0

Solving
9 + -22v + 8v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(1 + -2v)(9 + -4v) = 0

Subproblem 1
Set the factor '(1 + -2v)' equal to zero and attempt to solve:

Simplifying
1 + -2v = 0

Solving
1 + -2v = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2v = 0 + -1
-2v = 0 + -1

Combine like terms: 0 + -1 = -1
-2v = -1

Divide each side by '-2'.
v = 0.5

Simplifying
v = 0.5
Subproblem 2
Set the factor '(9 + -4v)' equal to zero and attempt to solve:

Simplifying
9 + -4v = 0

Solving
9 + -4v = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4v = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4v = 0 + -9
-4v = 0 + -9

Combine like terms: 0 + -9 = -9
-4v = -9

Divide each side by '-4'.
v = 2.25

Simplifying
v = 2.25
Solution
v = {0.5, 2.25}