Work the area of a rectangle out but already knowing the area and needing to know the length as it is two centermeters more than the width, area being 469

The area of a rectangle is the length times width:
a = l*w
the length is 2 centimeters more than the width:
l = w + 2
express area in terms of width
a = l*w
a = (w + 2)w
a = w^2 + 2w
w^2 + 2w = 469
w^2 + 2w - 469 = 0
we can solve using the general quadratic formula:
w = (-2 +- √(4 + 1876))/2
w = (-2 +- 43.36)/2
we use the positive solution:
w = (-2 + 43.36)/2
w = 20.68
thus the width is 20.68 cm
l = w + 2 = 20.68 + 2
l = 22.68
and the length is 22.68 cm