Question 18686
Start with the formula for the area of a rectangle:
{{{A = LW}}}
The new length is (8+x) ft. and the new width is (6+x) ft. The new area is:

{{{A = (8+x)(6+x)}}} = 120 ft^2

{{{(8+x)(6+x) = 120}}} Perform the indicated multiplication.
{{{48 + 14x + x^2 = 120}}} Rewite in standard form.
{{{x^2 + 14x - 72 = 0}}}Solve by factoring. 
{{{(x - 4)(x + 18) = 0}}} Apply the zero products principle.
{{{x - 4 = 0}}} and/or {{{x + 18 = 0}}}

If {{{x - 4 = 0}}}, then {{{x = 4}}}
If {{{x + 18 = 0}}}, then {{{x = -18}}} Discard this solution as not meaningful because the new length and width cannot be negative.

The new length is: {{{8 + 4 = 12}}} ft.
The new width is: {{{6 + 4 = 10}}} ft.

Check:

The new area is 120 ft^2

{{{A = (12)(10)}}} = 120 ft.^2