2v^2=9v+5

Solution for 2v^2=9v+5 equation:

Simplifying
2v2 = 9v + 5

Reorder the terms:
2v2 = 5 + 9v

Solving
2v2 = 5 + 9v

Solving for variable 'v'.

Reorder the terms:
-5 + -9v + 2v2 = 5 + 9v + -5 + -9v

Reorder the terms:
-5 + -9v + 2v2 = 5 + -5 + 9v + -9v

Combine like terms: 5 + -5 = 0
-5 + -9v + 2v2 = 0 + 9v + -9v
-5 + -9v + 2v2 = 9v + -9v

Combine like terms: 9v + -9v = 0
-5 + -9v + 2v2 = 0

Factor a trinomial.
(-1 + -2v)(5 + -1v) = 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 '(5 + -1v)' equal to zero and attempt to solve:

Simplifying
5 + -1v = 0

Solving
5 + -1v = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1v = 0 + -5
-1v = 0 + -5

Combine like terms: 0 + -5 = -5
-1v = -5

Divide each side by '-1'.
v = 5

Simplifying
v = 5
Solution
v = {-0.5, 5}