Solve for t h=6+29t-16t^2

$h = 6 + 29 t - 16 t^{2}$

Rewrite the equation as $6 + 29 t - 16 t^{2} = h$ .

$6 + 29 t - 16 t^{2} = h$

Move $h$ to the left side of the equation by subtracting it from both sides.

$6 + 29 t - 16 t^{2} - h = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = - 16$ , $b = 29$ , and $c = 6 - h$ into the quadratic formula and solve for $t$ .

$\frac{- 29 \pm \sqrt{29^{2} - 4 \cdot (- 16 \cdot (6 - h))}}{2 \cdot - 16}$

Simplify.

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Simplify the numerator.

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Raise $29$ to the power of $2$ .

$t = \frac{- 29 \pm \sqrt{841 - 4 \cdot (- 16 \cdot (6 - h))}}{2 \cdot - 16}$

Apply the distributive property.

$t = \frac{- 29 \pm \sqrt{841 - 4 \cdot (- 16 \cdot 6 - 16 (- h))}}{2 \cdot - 16}$

Multiply $- 16$ by $6$ .

$t = \frac{- 29 \pm \sqrt{841 - 4 \cdot (- 96 - 16 (- h))}}{2 \cdot - 16}$

Multiply $- 1$ by $- 16$ .

$t = \frac{- 29 \pm \sqrt{841 - 4 \cdot (- 96 + 16 h)}}{2 \cdot - 16}$

Apply the distributive property.

$t = \frac{- 29 \pm \sqrt{841 - 4 \cdot - 96 - 4 (16 h)}}{2 \cdot - 16}$

Multiply $- 4$ by $- 96$ .

$t = \frac{- 29 \pm \sqrt{841 + 384 - 4 (16 h)}}{2 \cdot - 16}$

Multiply $16$ by $- 4$ .

$t = \frac{- 29 \pm \sqrt{841 + 384 - 64 h}}{2 \cdot - 16}$

Add $841$ and $384$ .

$t = \frac{- 29 \pm \sqrt{1225 - 64 h}}{2 \cdot - 16}$

Multiply $2$ by $- 16$ .

$t = \frac{- 29 \pm \sqrt{1225 - 64 h}}{- 32}$

Simplify $\frac{- 29 \pm \sqrt{1225 - 64 h}}{- 32}$ .

$t = \frac{29 \pm \sqrt{1225 - 64 h}}{32}$

The final answer is the combination of both solutions.

$t = \frac{29 + \sqrt{1225 - 64 h}}{32}$

$t = \frac{29 - \sqrt{1225 - 64 h}}{32}$

Solve for t h=6+29t-16t^2

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