What value is a discontinuity of x squared plus 7 x plus 1, all over x squared plus 2 x minus 15?

(x^2+7x+1) / (x^2+2x-15)

A discontinuity, specifically a vertical asymptote, will occur when the denominator is equal to zero as division by zero is undefined.

(x^2+2x-15)

(x+5) (x-3)

So you will have two of them, when x=-5 and x=3