the length of a rectangle is 6 cm more than its width. Find its length and width when its area is 40 cm

Answer 1

width --- x
length --- x+6
x(x+6) = 42
x^2 + 6x - 42 = 0

x^2 + 9x + 9 = 42+9
(x+3)^2 = 51
x+3 = √51
x = √51 - 3 = appr 4.14

width is 4.14 , length is 10.14

check:
4.14(10.14) = appr 41.9796 , close enough for my round-off

I assume you know how to solve a quadratic that does not factor nicely.
I used completing the square instead of the formula.
If the middle term is even, that is easier and faster.