Solve for t h(t)=320-16t^2

$h (t) = 320 - 16 t^{2}$

Step 1

Add $16 t^{2}$ to both sides of the equation.

$h t + 16 t^{2} = 320$

Step 2

Subtract $320$ from both sides of the equation.

$h t + 16 t^{2} - 320 = 0$

Step 3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4

Substitute the values $a = 16$ , $b = h$ , and $c = - 320$ into the quadratic formula and solve for $t$ .

$\frac{- h \pm \sqrt{h^{2} - 4 \cdot (16 \cdot - 320)}}{2 \cdot 16}$

Step 5

Simplify.

Multiply $- 4 \cdot 16 \cdot - 320$ .

Multiply $- 4$ by $16$ .

$t = \frac{- h \pm \sqrt{h^{2} - 64 \cdot - 320}}{2 \cdot 16}$

Multiply $- 64$ by $- 320$ .

$t = \frac{- h \pm \sqrt{h^{2} + 20480}}{2 \cdot 16}$

Multiply $2$ by $16$ .

$t = \frac{- h \pm \sqrt{h^{2} + 20480}}{32}$

Step 6

The final answer is the combination of both solutions.

$t = - \frac{h - \sqrt{h^{2} + 20480}}{32}$

$t = - \frac{h + \sqrt{h^{2} + 20480}}{32}$