Find the x-intercept of the parabola with vertex (-1,2) and y-intercept (0,-3)

A graphing calculator shows the vertical scale factor is -5, so the equation is ...
   y = -5(x +1)² + 2

Then the x-intercepts are
   0 = -5(x +1)² + 2
   (x +1)² = 2/5
   x +1 = ±√(2/5)

   x = -1 ±√(2/5) ≈ {-1.63245553203, -0.36754446797}