Solve y=(7+x)123-7-x-1-x/2

$$y = ( 7 + x ) \frac { 123 - 7 - x - 1 - x } { 2 }$$

Solve for y

$$y=-\frac{\left(2x-115\right)\left(x+7\right)}{2}$$

Solution Steps

Subtract 7 from 123 to get 116.

$$y=\left(7+x\right)\times \frac{116-x-1-x}{2}$$

Subtract 1 from 116 to get 115.

$$y=\left(7+x\right)\times \frac{115-x-x}{2}$$

Combine -x and -x to get -2x.

$$y=\left(7+x\right)\times \frac{115-2x}{2}$$

Express \left(7+x\right)\times \frac{115-2x}{2} as a single fraction.

$$y=\frac{\left(7+x\right)\left(115-2x\right)}{2}$$

Use the distributive property to multiply 7+x by 115-2x and combine like terms.

$$y=\frac{805+101x-2x^{2}}{2}$$

Divide each term of 805+101x-2x^{2} by 2 to get \frac{805}{2}+\frac{101}{2}x-x^{2}.

$$y=\frac{805}{2}+\frac{101}{2}x-x^{2}$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{16641-16y}+101}{4}$$

$$x=\frac{\sqrt{16641-16y}+101}{4}$$

Solve for x

$$x=\frac{-\sqrt{16641-16y}+101}{4}$$

$$x=\frac{\sqrt{16641-16y}+101}{4}\text{, }y\leq \frac{16641}{16}$$