Y = v^2/2a solve for v

Solve for v:

Y = (a v^2) / 2

Y = (a v^2) / 2 is equivalent to (a v^2) / 2 = Y:

(a v^2) / 2 = Y

Divide both sides by a/2:

v^2 = (2 Y) / a

Take the square root of both sides:

Answer: v = sqrt (2) sqrt (Y/a) or v = - sqrt (2) sqrt (Y/a)