To solve this equation, we first need to simplify both sides by combining like terms.

26 + 5y - 0.5y^2 = 2.5y^2 + 26

Rearranging the terms, we get:

0.5y^2 + 5y - 2.5y^2 = 0

Combining like terms:

(0.5 - 2.5)y^2 + 5y = 0

-2y^2 + 5y = 0

Now, we can factor out a y from the equation:

y(-2y + 5) = 0

Setting each factor to zero:

y = 0 OR -2y + 5 = 0

Solving for y in the second equation:

-2y + 5 = 0
-2y = -5
y = 5/2

Therefore, the solutions to the equation are y = 0 and y = 5/2.