Thickness of the boundary layer generated on the flat plate

The shear stress produced in a thin sheet τwall, that is, when y = 0, is
given by the integral of the Von-Karman momentum:

$$
tau=-frac{d}{d x}left(int_{0}^{delta} rholeft(u^{2}-U uright) d yright)
$$

Suppose that the velocity profile within the boundary layer is quadratic and has the following
shape:

$$
u=a y+b y^{2}
$$
with the following boundary conditions:

$$
left.u(y)right|_{y=delta}=U,left.quad frac{partial u}{partial y}right|_{y=delta}=0
$$

Show that the thickness of the boundary layer generated on the flat plate is:

$$
delta approx 5.48 sqrt{operatorname{Re}_{x}} x
$$