Solve Using the Quadratic Formula 3x^2+75=0

$3 x^{2} + 75 = 0$

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 $c = 75$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (3 \cdot 75)}}{2 \cdot 3}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 3 \cdot 75}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot 75$ .

Multiply $- 4$ by $3$ .

$x = \frac{0 \pm \sqrt{0 - 12 \cdot 75}}{2 \cdot 3}$

Multiply $- 12$ by $75$ .

$x = \frac{0 \pm \sqrt{0 - 900}}{2 \cdot 3}$

Subtract $900$ from $0$ .

$x = \frac{0 \pm \sqrt{- 900}}{2 \cdot 3}$

Rewrite $- 900$ as $- 1 (900)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 900}}{2 \cdot 3}$

Rewrite $\sqrt{- 1 (900)}$ as $\sqrt{- 1} \cdot \sqrt{900}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{900}}{2 \cdot 3}$

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

$x = \frac{0 \pm i \cdot \sqrt{900}}{2 \cdot 3}$

Rewrite $900$ as $30^{2}$ .

$x = \frac{0 \pm i \cdot \sqrt{30^{2}}}{2 \cdot 3}$

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

$x = \frac{0 \pm i \cdot 30}{2 \cdot 3}$

Move $30$ to the left of $i$ .

$x = \frac{0 \pm 30 i}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{0 \pm 30 i}{6}$

Simplify $\frac{0 \pm 30 i}{6}$ .

$x = \pm 5 i$