Hello, mcinnes!
Did you make a sketch?
A rectangular garden measures 5m x 4m.
Its area is to be tripled by extending each dimension by the same amount.
How much should each dimension extend? Code:
: - - x+5 - - :
- *-------------* -
x | | :
- *---------* _ * - - - - * | :
: | | : | | | x+4
4 | 20 m² | 4 | | | :
: | | : | | | :
- *---------* - *---------*---* -
: - 5 - : : - 5 - : x :
The original garden is 5 by 4 and has an area of 20 m².
The new garden is $\displaystyle (x+5)$ by $\displaystyle (x+4)$ and has an area of 60 m².
There is our equation . . . .$\displaystyle (x+5)(x+4) \:=\:60 \quad\Rightarrow\quad x^2 + 9x - 40 \:=\:0$
Quadratic Formula: .$\displaystyle x \;=\;\frac{-9 \pm\sqrt{241}}{2} $
The positive root is: .$\displaystyle x \;=\;\frac{-9 + \sqrt{241}}{2} \;\approx\;3.262\text{ m}$