8) If sales value of x unit is 16.8 x and the cost of sales is \( -0.09 \mathrm{x}^{2}+1.8 \mathrm{x}+5000 \) then the number of units at break-even will be? \begin{tabular}{|l|l|l|l|}\hline a) 1200 & b) 800 & c) 333 & d) \( \mathbf{1 6 7} \) \\ \hline\end{tabular} 9) \( 25 x^{2}-\frac{500}{}=25 x \). Find the value of x ?

To find the break-even point, set the sales value equal to the cost of sales: \[ 16.8x = -0.09x^2 + 1.8x + 5000. \] Rearranging gives us: \[ 0.09x^2 + (16.8 - 1.8)x - 5000 = 0 \] or \[ 0.09x^2 + 15x - 5000 = 0. \] Now we can apply the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) where \( a = 0.09, b = 15, c = -5000 \). This will lead us to the break-even point where we find the number of units sold when total revenue equals total costs. Meanwhile, for the equation \( 25x^2 - 25x - 500 = 0 \), we simplify by dividing everything by 25: \[ x^2 - x - 20 = 0. \] Factoring gives us \( (x - 5)(x + 4) = 0 \), leading to solutions \( x = 5 \) or \( x = -4 \). Since we typically can't have a negative quantity, the value of \( x \) is 5!