Solve Using the Quadratic Formula 3y^2-1=0

$3 y^{2} - 1 = 0$

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 $a = 3$ , $b = 0$ , and $c = - 1$ into the quadratic formula and solve for $y$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (3 \cdot - 1)}}{2 \cdot 3}$

Step 3

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$y = \frac{0 \pm \sqrt{0 - 4 \cdot 3 \cdot - 1}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot - 1$ .

Multiply $- 4$ by $3$ .

$y = \frac{0 \pm \sqrt{0 - 12 \cdot - 1}}{2 \cdot 3}$

Multiply $- 12$ by $- 1$ .

$y = \frac{0 \pm \sqrt{0 + 12}}{2 \cdot 3}$

Add $0$ and $12$ .

$y = \frac{0 \pm \sqrt{12}}{2 \cdot 3}$

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$y = \frac{0 \pm \sqrt{4 (3)}}{2 \cdot 3}$

Rewrite $4$ as $2^{2}$ .

$y = \frac{0 \pm \sqrt{2^{2} \cdot 3}}{2 \cdot 3}$

Pull terms out from under the radical.

$y = \frac{0 \pm 2 \sqrt{3}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$y = \frac{0 \pm 2 \sqrt{3}}{6}$

Simplify $\frac{0 \pm 2 \sqrt{3}}{6}$ .

$y = \frac{\pm \sqrt{3}}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{\pm \sqrt{3}}{3}$

Decimal Form:

$y = 0.57735026 \dots, - 0.57735026 \dots$