Solve W=left(3/4t+34-20right)left(-t+52right)

$$W = \left( \frac{ 3 }{ 4 } t+34-20 \right) \left( -t+52 \right)$$

Solve for W

$$W=-\frac{\left(t-52\right)\left(3t+56\right)}{4}$$

Solution Steps

Subtract 20 from 34 to get 14.

$$W=\left(\frac{3}{4}t+14\right)\left(-t+52\right)$$

Use the distributive property to multiply \frac{3}{4}t+14 by -t+52.

$$W=\frac{3}{4}t\left(-t\right)+39t+14\left(-t\right)+728$$

Multiply t and t to get t^{2}.

$$W=\frac{3}{4}t^{2}\left(-1\right)+39t+14\left(-1\right)t+728$$

Multiply \frac{3}{4} and -1 to get -\frac{3}{4}.

$$W=-\frac{3}{4}t^{2}+39t+14\left(-1\right)t+728$$

Multiply 14 and -1 to get -14.

$$W=-\frac{3}{4}t^{2}+39t-14t+728$$

Combine 39t and -14t to get 25t.

$$W=-\frac{3}{4}t^{2}+25t+728$$

Solve for t (complex solution)

$$t=\frac{2\sqrt{2809-3W}+50}{3}$$

$$t=\frac{-2\sqrt{2809-3W}+50}{3}$$

Solve for t

$$t=\frac{2\sqrt{2809-3W}+50}{3}$$

$$t=\frac{-2\sqrt{2809-3W}+50}{3}\text{, }W\leq \frac{2809}{3}$$