The length of the top of a table is 7 m greater than the width. the area is 78 msquared . find the dimensions of the table.

Let x = width (m) of the table.
Because the length is 7 m greater than the width, therefore
length = (x + 7) m.

The area is width x length, therefore
x(x+7) = 78
x^2 + 7x = 78
x^2 + 7x - 78 = 0
This is a quadratic equation.

Note that 78 = 6*13, and 13 - 6 = 7.

Factorizethe quadratic equation to obtain
(x - 6)(x + 13) = 0
The solution is x = 6, or x = -13

Because we cannot have negative length, discard the negative answer.

The width is 6 m
The length is 6+7 = 13 m