Solve Using the Quadratic Formula 29=57t-5t^2

$29 = 57 t - 5 t^{2}$

Step 1

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

Subtract $57 t$ from both sides of the equation.

$29 - 57 t = - 5 t^{2}$

Add $5 t^{2}$ to both sides of the equation.

$29 - 57 t + 5 t^{2} = 0$

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 $a = 5$ , $b = - 57$ , and $c = 29$ into the quadratic formula and solve for $t$ .

$\frac{57 \pm \sqrt{{(- 57)}^{2} - 4 \cdot (5 \cdot 29)}}{2 \cdot 5}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 57$ to the power of $2$ .

$t = \frac{57 \pm \sqrt{3249 - 4 \cdot 5 \cdot 29}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot 29$ .

Multiply $- 4$ by $5$ .

$t = \frac{57 \pm \sqrt{3249 - 20 \cdot 29}}{2 \cdot 5}$

Multiply $- 20$ by $29$ .

$t = \frac{57 \pm \sqrt{3249 - 580}}{2 \cdot 5}$

Subtract $580$ from $3249$ .

$t = \frac{57 \pm \sqrt{2669}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$t = \frac{57 \pm \sqrt{2669}}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = \frac{57 \pm \sqrt{2669}}{10}$

Decimal Form:

$t = 10.86623654 \dots, 0.53376345 \dots$