Solve Using the Quadratic Formula 3x^2-6x+8=0

$3 x^{2} - 6 x + 8 = 0$

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 $a = 3$ , $b = - 6$ , and $c = 8$ into the quadratic formula and solve for $x$ .

$\frac{6 \pm \sqrt{{(- 6)}^{2} - 4 \cdot (3 \cdot 8)}}{2 \cdot 3}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 6$ to the power of $2$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 3 \cdot 8}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot 8$ .

Multiply $- 4$ by $3$ .

$x = \frac{6 \pm \sqrt{36 - 12 \cdot 8}}{2 \cdot 3}$

Multiply $- 12$ by $8$ .

$x = \frac{6 \pm \sqrt{36 - 96}}{2 \cdot 3}$

Subtract $96$ from $36$ .

$x = \frac{6 \pm \sqrt{- 60}}{2 \cdot 3}$

Rewrite $- 60$ as $- 1 (60)$ .

$x = \frac{6 \pm \sqrt{- 1 \cdot 60}}{2 \cdot 3}$

Rewrite $\sqrt{- 1 (60)}$ as $\sqrt{- 1} \cdot \sqrt{60}$ .

$x = \frac{6 \pm \sqrt{- 1} \cdot \sqrt{60}}{2 \cdot 3}$

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

$x = \frac{6 \pm i \cdot \sqrt{60}}{2 \cdot 3}$

Rewrite $60$ as $2^{2} \cdot 15$ .

Factor $4$ out of $60$ .

$x = \frac{6 \pm i \cdot \sqrt{4 (15)}}{2 \cdot 3}$

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

$x = \frac{6 \pm i \cdot \sqrt{2^{2} \cdot 15}}{2 \cdot 3}$

Pull terms out from under the radical.

$x = \frac{6 \pm i \cdot (2 \sqrt{15})}{2 \cdot 3}$

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

$x = \frac{6 \pm 2 i \sqrt{15}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{6 \pm 2 i \sqrt{15}}{6}$

Simplify $\frac{6 \pm 2 i \sqrt{15}}{6}$ .

$x = \frac{3 \pm i \sqrt{15}}{3}$