Solve using the quadratic formula.

-v^2 + 9v - 5 = 0

v = 9/2 + sqrt (61) / 2 or v = 9/2 - sqrt (61) / 2

Step-by-step explanation:

Solve for v over the real numbers:

-v^2 + 9 v - 5 = 0

Multiply both sides by - 1:

v^2 - 9 v + 5 = 0

Subtract 5 from both sides:

v^2 - 9 v = - 5

Add 81/4 to both sides:

v^2 - 9 v + 81/4 = 61/4

Write the left hand side as a square:

(v - 9/2) ^2 = 61/4

Take the square root of both sides:

v - 9/2 = sqrt (61) / 2 or v - 9/2 = - sqrt (61) / 2

Add 9/2 to both sides:

v = 9/2 + sqrt (61) / 2 or v - 9/2 = - sqrt (61) / 2

Add 9/2 to both sides:

Answer: v = 9/2 + sqrt (61) / 2 or v = 9/2 - sqrt (61) / 2