3.74: Line, curve and tangent intersection

The diagram shows the line $y = 1 - 4x$ meeting the curve $y = 4x^{2} - 6x - 5$ at the points $A$ and $B$. The tangent to the curve at $B$ meets the horizontal line through $A$ at the point $C$. Find the $x$-coordinate of $C$, giving your answer correct to $2$ decimal places.