Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$2^{x} \left(4 x - 7\right) = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = \frac{7}{4}$$
Numerical solution$$x_{1} = -130.560173892367$$
$$x_{2} = -104.674166405026$$
$$x_{3} = -100.698060959641$$
$$x_{4} = -57.294975833538$$
$$x_{5} = -70.9940544810989$$
$$x_{6} = -53.4287790344014$$
$$x_{7} = -55.3579282831068$$
$$x_{8} = -102.685831208952$$
$$x_{9} = -76.9102986733328$$
$$x_{10} = -128.567045505463$$
$$x_{11} = -116.61410475038$$
$$x_{12} = 1.75$$
$$x_{13} = -118.605484638325$$
$$x_{14} = -124.581558957354$$
$$x_{15} = -110.642193130371$$
$$x_{16} = -78.8861273471272$$
$$x_{17} = -106.663028005667$$
$$x_{18} = -92.7535477155393$$
$$x_{19} = -47.7084257679483$$
$$x_{20} = -98.7108980899914$$
$$x_{21} = -84.8224250368008$$
$$x_{22} = -120.597199566848$$
$$x_{23} = -122.589230274903$$
$$x_{24} = -72.9640484285695$$
$$x_{25} = -80.8635210365604$$
$$x_{26} = -49.6014171256296$$
$$x_{27} = -112.632435356791$$
$$x_{28} = -65.0999900791222$$
$$x_{29} = -108.652380920465$$
$$x_{30} = -126.574169129318$$
$$x_{31} = -96.724389431829$$
$$x_{32} = -63.1418710289193$$
$$x_{33} = -86.8036898586515$$
$$x_{34} = -114.62308077281$$
$$x_{35} = -82.8423304777736$$
$$x_{36} = -90.7693361469761$$
$$x_{37} = -59.238627125049$$
$$x_{38} = -69.026493050923$$
$$x_{39} = -51.5092035175383$$
$$x_{40} = -74.9362064115449$$
$$x_{41} = -61.1878635487672$$
$$x_{42} = -88.786023529583$$
$$x_{43} = -94.738586806713$$
$$x_{44} = -67.061680055888$$