Solve (t)=80k-16t^2

$$( t ) = 80 k - 16 t ^ { 2 }$$

Solve for k

$$k=\frac{t\left(16t+1\right)}{80}$$

Steps for Solving Linear Equation

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

$$80k-16t^{2}=t$$

Add 16t^{2} to both sides.

$$80k=t+16t^{2}$$

The equation is in standard form.

$$80k=16t^{2}+t$$

Divide both sides by 80.

$$\frac{80k}{80}=\frac{t\left(16t+1\right)}{80}$$

Dividing by 80 undoes the multiplication by 80.

$$k=\frac{t\left(16t+1\right)}{80}$$

Divide t\left(1+16t\right) by 80.

$$k=\frac{t^{2}}{5}+\frac{t}{80}$$

Solve for t (complex solution)

$$t=\frac{\sqrt{5120k+1}-1}{32}$$

$$t=\frac{-\sqrt{5120k+1}-1}{32}$$

Solve for t

$$t=\frac{\sqrt{5120k+1}-1}{32}$$

$$t=\frac{-\sqrt{5120k+1}-1}{32}\text{, }k\geq -\frac{1}{5120}$$