Solve -16t^2+80T+3.5t=0

$$- 16 t ^ { 2 } + 80 T + 3.5 t = 0$$

Solve for T

$$T=\frac{t\left(32t-7\right)}{160}$$

Steps for Solving Linear Equation

Add 16t^{2} to both sides. Anything plus zero gives itself.

$$80T+3.5t=16t^{2}$$

Subtract 3.5t from both sides.

$$80T=16t^{2}-3.5t$$

The equation is in standard form.

$$80T=16t^{2}-\frac{7t}{2}$$

Divide both sides by 80.

$$\frac{80T}{80}=\frac{t\left(16t-3.5\right)}{80}$$

Dividing by 80 undoes the multiplication by 80.

$$T=\frac{t\left(16t-3.5\right)}{80}$$

Divide t\left(-3.5+16t\right) by 80.

$$T=\frac{t^{2}}{5}-\frac{7t}{160}$$

Solve for t (complex solution)

$$t=-\frac{\sqrt{5120T+12.25}}{32}+0.109375$$

$$t=\frac{\sqrt{5120T+12.25}}{32}+0.109375$$

Solve for t

$$t=-\frac{\sqrt{5120T+12.25}}{32}+0.109375$$

$$t=\frac{\sqrt{5120T+12.25}}{32}+0.109375\text{, }T\geq -\frac{49}{20480}$$