Solve by using the quadratic formula. The area of a rectangular plot is $528 \ m^2$. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

(16 M, 33 M) Let the breadth of the plot be $x \ m$. Then the length is $(2x + 1) \ m$.
Given that the area is $528 \ m^2$,we have $x(2x + 1) = 528$,which simplifies to $2x^2 + x - 528 = 0$.
This is a quadratic equation of the form $ax^2 + bx + c = 0$,where $a = 2, b = 1, c = -528$.
Using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$:
$x = \frac{-1 \pm \sqrt{1^2 - 4(2)(-528)}}{2(2)} = \frac{-1 \pm \sqrt{1 + 4224}}{4} = \frac{-1 \pm \sqrt{4225}}{4} = \frac{-1 \pm 65}{4}$.
This gives two possible values for $x$: $x = \frac{64}{4} = 16$ or $x = \frac{-66}{4} = -16.5$.
Since the breadth cannot be negative,we take $x = 16 \ m$.
Therefore,the breadth is $16 \ m$ and the length is $2(16) + 1 = 33 \ m$.