Solve y=(2x-a)x+170(70-x)+160(40-x)+150(x-10)

$$y = ( 2 x - a ) x + 170 ( 70 - x ) + 160 ( 40 - x ) + 150 ( x - 10 )$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{2x^{2}-180x-y+16800}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&y=16800\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-a by x.

$$y=2x^{2}-ax+170\left(70-x\right)+160\left(40-x\right)+150\left(x-10\right)$$

Use the distributive property to multiply 170 by 70-x.

$$y=2x^{2}-ax+11900-170x+160\left(40-x\right)+150\left(x-10\right)$$

Use the distributive property to multiply 160 by 40-x.

$$y=2x^{2}-ax+11900-170x+6400-160x+150\left(x-10\right)$$

Add 11900 and 6400 to get 18300.

$$y=2x^{2}-ax+18300-170x-160x+150\left(x-10\right)$$

Combine -170x and -160x to get -330x.

$$y=2x^{2}-ax+18300-330x+150\left(x-10\right)$$

Use the distributive property to multiply 150 by x-10.

$$y=2x^{2}-ax+18300-330x+150x-1500$$

Combine -330x and 150x to get -180x.

$$y=2x^{2}-ax+18300-180x-1500$$

Subtract 1500 from 18300 to get 16800.

$$y=2x^{2}-ax+16800-180x$$

Swap sides so that all variable terms are on the left hand side.

$$2x^{2}-ax+16800-180x=y$$

Subtract 2x^{2} from both sides.

$$-ax+16800-180x=y-2x^{2}$$

Subtract 16800 from both sides.

$$-ax-180x=y-2x^{2}-16800$$

Add 180x to both sides.

$$-ax=y-2x^{2}-16800+180x$$

The equation is in standard form.

$$\left(-x\right)a=-2x^{2}+180x+y-16800$$

Divide both sides by -x.

$$\frac{\left(-x\right)a}{-x}=\frac{-2x^{2}+180x+y-16800}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$a=\frac{-2x^{2}+180x+y-16800}{-x}$$

Divide y-16800+180x-2x^{2} by -x.

$$a=2x+\frac{16800-y}{x}-180$$

Solve for a

$$\left\{\begin{matrix}a=\frac{2x^{2}-180x-y+16800}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&y=16800\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-a by x.

$$y=2x^{2}-ax+170\left(70-x\right)+160\left(40-x\right)+150\left(x-10\right)$$

Use the distributive property to multiply 170 by 70-x.

$$y=2x^{2}-ax+11900-170x+160\left(40-x\right)+150\left(x-10\right)$$

Use the distributive property to multiply 160 by 40-x.

$$y=2x^{2}-ax+11900-170x+6400-160x+150\left(x-10\right)$$

Add 11900 and 6400 to get 18300.

$$y=2x^{2}-ax+18300-170x-160x+150\left(x-10\right)$$

Combine -170x and -160x to get -330x.

$$y=2x^{2}-ax+18300-330x+150\left(x-10\right)$$

Use the distributive property to multiply 150 by x-10.

$$y=2x^{2}-ax+18300-330x+150x-1500$$

Combine -330x and 150x to get -180x.

$$y=2x^{2}-ax+18300-180x-1500$$

Subtract 1500 from 18300 to get 16800.

$$y=2x^{2}-ax+16800-180x$$

Swap sides so that all variable terms are on the left hand side.

$$2x^{2}-ax+16800-180x=y$$

Subtract 2x^{2} from both sides.

$$-ax+16800-180x=y-2x^{2}$$

Subtract 16800 from both sides.

$$-ax-180x=y-2x^{2}-16800$$

Add 180x to both sides.

$$-ax=y-2x^{2}-16800+180x$$

The equation is in standard form.

$$\left(-x\right)a=-2x^{2}+180x+y-16800$$

Divide both sides by -x.

$$\frac{\left(-x\right)a}{-x}=\frac{-2x^{2}+180x+y-16800}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$a=\frac{-2x^{2}+180x+y-16800}{-x}$$

Divide y-16800+180x-2x^{2} by -x.

$$a=2x+\frac{16800-y}{x}-180$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{8y+a^{2}+360a-102000}+a+180}{4}$$

$$x=\frac{\sqrt{8y+a^{2}+360a-102000}+a+180}{4}$$

Solve for x

$$x=\frac{-\sqrt{8y+a^{2}+360a-102000}+a+180}{4}$$

$$x=\frac{\sqrt{8y+a^{2}+360a-102000}+a+180}{4}\text{, }y\geq -\frac{a^{2}}{8}-45a+12750$$