Solve Using the Quadratic Formula 0=-16t^2+48t+64

$0 = - 16 t^{2} + 48 t + 64$

Step 1

Move all the expressions to the left side of the equation.

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

$16 t^{2} = 48 t + 64$

Subtract $48 t$ from both sides of the equation.

$16 t^{2} - 48 t = 64$

Subtract $64$ from both sides of the equation.

$16 t^{2} - 48 t - 64 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = 16$ , $b = - 48$ , and $c = - 64$ into the quadratic formula and solve for $t$ .

$\frac{48 \pm \sqrt{{(- 48)}^{2} - 4 \cdot (16 \cdot - 64)}}{2 \cdot 16}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 48$ to the power of $2$ .

$t = \frac{48 \pm \sqrt{2304 - 4 \cdot 16 \cdot - 64}}{2 \cdot 16}$

Multiply $- 4 \cdot 16 \cdot - 64$ .

Multiply $- 4$ by $16$ .

$t = \frac{48 \pm \sqrt{2304 - 64 \cdot - 64}}{2 \cdot 16}$

Multiply $- 64$ by $- 64$ .

$t = \frac{48 \pm \sqrt{2304 + 4096}}{2 \cdot 16}$

Add $2304$ and $4096$ .

$t = \frac{48 \pm \sqrt{6400}}{2 \cdot 16}$

Rewrite $6400$ as $80^{2}$ .

$t = \frac{48 \pm \sqrt{80^{2}}}{2 \cdot 16}$

Pull terms out from under the radical, assuming positive real numbers.

$t = \frac{48 \pm 80}{2 \cdot 16}$

Multiply $2$ by $16$ .

$t = \frac{48 \pm 80}{32}$

Simplify $\frac{48 \pm 80}{32}$ .

$t = \frac{3 \pm 5}{2}$

Step 5

The final answer is the combination of both solutions.

$t = 4, - 1$