Question 1005957
The three TERMS for the series are shown.
Successive ratios must be equal.


{{{highlight_green((7-5x)/6=6/(3-x))}}}, the successive ratios
{{{(7-5x)(3-x)=36}}}
{{{21-15x-7x+5x^2-36=0}}}
{{{5x^2-22x+21-36=0}}}
{{{5x^2-22x-15=0}}}


General solution formula for a quadratic equation gives
{{{x=(22+- sqrt(22^2-4*5*(-15)))/(2*5)}}}
{{{x=(22+- sqrt(22^2+20*15))/(2*5)}}}

{{{x=(22+- sqrt(784))/10}}}
{{{x=(22+- 28)/10}}}
{{{x=(11+- 14)/5}}}
{{{highlight(x=-3/5)}}}  OR  {{{highlight(x=5)}}}