Solve Using the Quadratic Formula 2x^2+3=0

$2 x^{2} + 3 = 0$

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 $a = 2$ , $b = 0$ , and $c = 3$ into the quadratic formula and solve for $x$ .

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

Step 3

Simplify.

Simplify the numerator.

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

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

Multiply $- 4 \cdot 2 \cdot 3$ .

Multiply $- 4$ by $2$ .

$x = \frac{0 \pm \sqrt{0 - 8 \cdot 3}}{2 \cdot 2}$

Multiply $- 8$ by $3$ .

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

Subtract $24$ from $0$ .

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

Rewrite $- 24$ as $- 1 (24)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 24}}{2 \cdot 2}$

Rewrite $\sqrt{- 1 (24)}$ as $\sqrt{- 1} \cdot \sqrt{24}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{24}}{2 \cdot 2}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{0 \pm i \cdot \sqrt{24}}{2 \cdot 2}$

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

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

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

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

Pull terms out from under the radical.

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

Move $2$ to the left of $i$ .

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

Multiply $2$ by $2$ .

$x = \frac{0 \pm 2 i \sqrt{6}}{4}$

Simplify $\frac{0 \pm 2 i \sqrt{6}}{4}$ .

$x = \frac{\pm i \sqrt{6}}{2}$