Question 1199809
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The reciprocal function is  f(x) = {{{1/(5x^2 + 13x - 6)}}}.


Vertical asymptotes are where the denominator polynomial has zeroes.


In the denominator, you have a quadratic function.


Its zeroes are the root of this polynomial.


Find the roots using the quadratic formula


    {{{x[1,2]}}} = {{{(-13 +- sqrt(13^2 - 4*5*(-6)))/(2*5)}}} = {{{(-13 +- sqrt(289))/10}}} = {{{(-13 +- 17)/10}}}.


The roots are   -3  and  {{{4/10}}} = 0.4 = {{{2/5}}}.


So, vertical asymptotes are  x = -3  and  x = {{{4/10}}} = 0.4 = {{{2/5}}}.
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Solved, with full explanations.