Solve y=(20-x-200/20)(x-80)

$$y = ( 20 - \frac { x - 200 } { 20 } ) ( x - 80 )$$

Solve for y

$$y=-\frac{\left(x-600\right)\left(x-80\right)}{20}$$

Solution Steps

Use the distributive property to multiply 20-\frac{x-200}{20} by x-80.

$$y=20x-1600+\left(-\frac{x-200}{20}\right)x-80\left(-\frac{x-200}{20}\right)$$

Express \left(-\frac{x-200}{20}\right)x as a single fraction.

$$y=20x-1600+\frac{-\left(x-200\right)x}{20}-80\left(-\frac{x-200}{20}\right)$$

Multiply -80 and -1 to get 80.

$$y=20x-1600+\frac{-\left(x-200\right)x}{20}+80\times \frac{x-200}{20}$$

Use the distributive property to multiply -1 by x-200.

$$y=20x-1600+\frac{\left(-x+200\right)x}{20}+80\times \frac{x-200}{20}$$

Use the distributive property to multiply -x+200 by x.

$$y=20x-1600+\frac{-x^{2}+200x}{20}+80\times \frac{x-200}{20}$$

Cancel out 20, the greatest common factor in 80 and 20.

$$y=20x-1600+\frac{-x^{2}+200x}{20}+4\left(x-200\right)$$

Use the distributive property to multiply 4 by x-200.

$$y=20x-1600+\frac{-x^{2}+200x}{20}+4x-800$$

Combine 20x and 4x to get 24x.

$$y=24x-1600+\frac{-x^{2}+200x}{20}-800$$

Subtract 800 from -1600 to get -2400.

$$y=24x-2400+\frac{-x^{2}+200x}{20}$$

Divide each term of -x^{2}+200x by 20 to get -\frac{1}{20}x^{2}+10x.

$$y=24x-2400-\frac{1}{20}x^{2}+10x$$

Combine 24x and 10x to get 34x.

$$y=34x-2400-\frac{1}{20}x^{2}$$

Solve for x (complex solution)

$$x=2\sqrt{16900-5y}+340$$

$$x=-2\sqrt{16900-5y}+340$$

Solve for x

$$x=2\sqrt{16900-5y}+340$$

$$x=-2\sqrt{16900-5y}+340\text{, }y\leq 3380$$