1 + 2 + 3 + ... + x = 55
=> (x + 1) . x : 2 = 55
=> (x + 1) . x = 55 . 2
=> (x + 1) . x = 110
=> (x + 1) . x = 11 . 10
=> (x + 1) . x = (10 + 1) . 10
=> x = 10.
<=> x(x + 1) : 2 = 55
<=> x(x + 1) = 55.2
<=> x(x + 1) = 110
<=> x(x + 1) = 10.11
<=> x(x + 1) = 10(10 + 1)
=> x = 10