Solve y=(-1/2t+50-6)(2t+100)

$$y = ( - \frac { 1 } { 2 } t + 50 - 6 ) ( 2 t + 100 )$$

Solve for y

$$y=-\left(t-88\right)\left(t+50\right)$$

Solution Steps

Subtract 6 from 50 to get 44.

$$y=\left(-\frac{1}{2}t+44\right)\left(2t+100\right)$$

Use the distributive property to multiply -\frac{1}{2}t+44 by 2t+100 and combine like terms.

$$y=-t^{2}+38t+4400$$

Solve for t (complex solution)

$$t=\sqrt{4761-y}+19$$

$$t=-\sqrt{4761-y}+19$$

Solve for t

$$t=\sqrt{4761-y}+19$$

$$t=-\sqrt{4761-y}+19\text{, }y\leq 4761$$