Question 113214
{{{N=4x^2+5x+1}}} is the given function.  We want to know x when N = 175.  So,


{{{4x^2+5x+1=175}}}
{{{4x^2+5x+1-175=0}}}, subtract 175 from both sides
{{{4x^2+5x-174=0}}}, collect terms

As it happens, this trinomial is factorable:
{{{4x^2+5x-174=(4x+29)(x-6)}}}, so
{{{(4x+29)(x-6)=0}}}, and 


{{{x=6}}} or
{{{x=-29/4}}}

A negative number of years in this case would be absurd, so you can exclude the negative result.  The answer is 6 years.


Hope this helps,
John