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the length of a swimming pool is 8m longer than it's width and the area is 105msquared .

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AnneCviz
Let x be the width
     x+8 be the length

A = w·l

Substitute the given,
105 = x (x+8)
105 = x² + 8x
0 = x² + 8x -105
0 = (x+15) (x-7)
x = -15  ; x = 7       [Use x=7 since there is no negative dimension]

Width = 7m
Length = 15m         [from x+8]