Solve Using the Quadratic Formula 6x^2-5=0

$6 x^{2} - 5 = 0$

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 $a = 6$ , $b = 0$ , and $c = - 5$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (6 \cdot - 5)}}{2 \cdot 6}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 6 \cdot - 5}}{2 \cdot 6}$

Multiply $- 4 \cdot 6 \cdot - 5$ .

Multiply $- 4$ by $6$ .

$x = \frac{0 \pm \sqrt{0 - 24 \cdot - 5}}{2 \cdot 6}$

Multiply $- 24$ by $- 5$ .

$x = \frac{0 \pm \sqrt{0 + 120}}{2 \cdot 6}$

Add $0$ and $120$ .

$x = \frac{0 \pm \sqrt{120}}{2 \cdot 6}$

Rewrite $120$ as $2^{2} \cdot 30$ .

Factor $4$ out of $120$ .

$x = \frac{0 \pm \sqrt{4 (30)}}{2 \cdot 6}$

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

$x = \frac{0 \pm \sqrt{2^{2} \cdot 30}}{2 \cdot 6}$

Pull terms out from under the radical.

$x = \frac{0 \pm 2 \sqrt{30}}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{0 \pm 2 \sqrt{30}}{12}$

Simplify $\frac{0 \pm 2 \sqrt{30}}{12}$ .

$x = \frac{\pm \sqrt{30}}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\pm \sqrt{30}}{6}$

Decimal Form:

$x = 0.91287092 \dots, - 0.91287092 \dots$