If you draw a graph of the current then I think from your description that will be a straight line with y intercept at 4 and a slope of -7.
From t=0 to t=4/7 there will be current (charge) flowing into the circuit.
To find where the cumulative charge is zero the area in the triangle above the x axis and below the line must equal the area in the triangle below the x axis and above the line. It seems that will happen when x=2*4/7.
The WolframAlpha plot of the integral shows two orange points where the charge is zero, one when t=0 and the other when t=8/7 or 1.1428 microseconds which seems to match this description.
Is there any chance there is something in the description of the problem that needs to be changed? Or did I misunderstand something?