Question 751370
If x-3 is actually a root for v(x), then you could more easily factor the function.  Try synthetic division by (x-3).  See what this allows you to do.  I have not tried all this yet but it might be all you need.  

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I'm not getting anything like what you say is the answer.  That "x-3" seems to be no help.  At holding 70 cubic meters, {{{v=x^3-16x^2+79x-120=70}}};
{{{x^3-16x^2+79x-120-70=0}}}
{{{x^3-16x^2+79x-190=0}}}
Trying synthetic division according to Factor Theorem {{{(x-10)(x^2-6x+19)=0}}} so a rational root is 10.  The quadratic factor has imaginary parts.  

{{{x=10}}} if this aquarium holds 70 m^3, and the depth is {{{x-3=10-3=7}}} meters.