The rule for this special form of quadratic equation is:
(color(red)(x) - color(blue)(y))^2 = (color(red)(x) - color(blue)(y))(color(red)(x) - color(blue)(y)) = color(red)(x)^2 - 2color(red)(x)color(blue)(y) + color(blue)(y)^2
Substitute:
color(red)(sqrt(a)) for color(red)(x)
color(blue)(sqrt(5)) for color(blue)(y)
Giving:
(color(red)(sqrt(a)) - color(blue)(sqrt(5)))^2 =>
(color(red)(sqrt(a)) - color(blue)(sqrt(5)))(color(red)(sqrt(a)) - color(blue)(sqrt(5))) =>
(color(red)(sqrt(a)))^2 - 2color(red)(sqrt(a))color(blue)(sqrt(5)) + (color(blue)(sqrt(5)))^2 =>
color(red)(a) - 2sqrt(color(red)(a)color(blue)(5)) + color(blue)(5)
