There are more ways to solve the quadratic equation.

The provided solution is not using the quadratic formula but factoring of polynomial:

And then we apply Zero-product property: 

'If ab = 0, then either a = 0 or b = 0'

So the solutions are obtained from:

x - 5 = 0

x = 5

One solution is x1 = 5

x - 1 = 0

x = 1

Second solution is x2 = 1