Solve for t h(t)=-16t^2+64

$h (t) = - 16 t^{2} + 64$

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

$h t + 16 t^{2} = 64$

Subtract $64$ from both sides of the equation.

$h t + 16 t^{2} - 64 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 16$ , $b = h$ , and $c = - 64$ into the quadratic formula and solve for $t$ .

$\frac{- h \pm \sqrt{h^{2} - 4 \cdot (16 \cdot - 64)}}{2 \cdot 16}$

Simplify.

Simplify the numerator.

Multiply $- 4$ by $16$ .

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

Multiply $- 64$ by $- 64$ .

$t = \frac{- h \pm \sqrt{h^{2} + 4096}}{2 \cdot 16}$

Multiply $2$ by $16$ .

$t = \frac{- h \pm \sqrt{h^{2} + 4096}}{32}$

The final answer is the combination of both solutions.

$t = - \frac{h - \sqrt{h^{2} + 4096}}{32}$

$t = - \frac{h + \sqrt{h^{2} + 4096}}{32}$