I would appreciate any help with the following problem.
Hello, pashah!
$\displaystyle y - 1 \:= \:\sqrt{\frac{y+1}{4}}$
Square both sides: .$\displaystyle (y-1)^2\:=\:\frac{y+1}{4}$
We have: .$\displaystyle y^2 - 2y + 1 \:= \:\frac{y+1}{4}$
Multiply by 4: .$\displaystyle 4y^2 - 8y + 4\:=\:y + 1\quad\Rightarrow\quad 4y^2 - 9y + 3 \:= \:0$
Now use the Quadratic Formula . . .