Solve Using the Quadratic Formula 14s^2-21s=0

$14 s^{2} - 21 s = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 14$ , $b = - 21$ , and $c = 0$ into the quadratic formula and solve for $s$ .

$\frac{21 \pm \sqrt{{(- 21)}^{2} - 4 \cdot (14 \cdot 0)}}{2 \cdot 14}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 21$ to the power of $2$ .

$s = \frac{21 \pm \sqrt{441 - 4 \cdot 14 \cdot 0}}{2 \cdot 14}$

Multiply $- 4 \cdot 14 \cdot 0$ .

Multiply $- 4$ by $14$ .

$s = \frac{21 \pm \sqrt{441 - 56 \cdot 0}}{2 \cdot 14}$

Multiply $- 56$ by $0$ .

$s = \frac{21 \pm \sqrt{441 + 0}}{2 \cdot 14}$

Add $441$ and $0$ .

$s = \frac{21 \pm \sqrt{441}}{2 \cdot 14}$

Rewrite $441$ as $21^{2}$ .

$s = \frac{21 \pm \sqrt{21^{2}}}{2 \cdot 14}$

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

$s = \frac{21 \pm 21}{2 \cdot 14}$

Multiply $2$ by $14$ .

$s = \frac{21 \pm 21}{28}$

Simplify $\frac{21 \pm 21}{28}$ .

$s = \frac{3 \pm 3}{4}$

Step 4

The final answer is the combination of both solutions.

$s = \frac{3}{2}, 0$