Quadrilaterals & Polygons · Medium problem

The diagonals of rectangle $ABCD$ meet at $E$. If $AE = 4x-3$ and the full diagonal $BD = 6x+2$, find $x$ and the length of diagonal $\overline{AC}$. (Diagonals of a rectangle are congruent and bisect each other, so $AE = \tfrac12 BD$.)