Solve Using the Quadratic Formula 3x^2+x+10=0

$3 x^{2} + x + 10 = 0$

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 $a = 3$ , $b = 1$ , and $c = 10$ into the quadratic formula and solve for $x$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (3 \cdot 10)}}{2 \cdot 3}$

Step 3

Simplify.

Simplify the numerator.

One to any power is one.

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 3 \cdot 10}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot 10$ .

Multiply $- 4$ by $3$ .

$x = \frac{- 1 \pm \sqrt{1 - 12 \cdot 10}}{2 \cdot 3}$

Multiply $- 12$ by $10$ .

$x = \frac{- 1 \pm \sqrt{1 - 120}}{2 \cdot 3}$

Subtract $120$ from $1$ .

$x = \frac{- 1 \pm \sqrt{- 119}}{2 \cdot 3}$

Rewrite $- 119$ as $- 1 (119)$ .

$x = \frac{- 1 \pm \sqrt{- 1 \cdot 119}}{2 \cdot 3}$

Rewrite $\sqrt{- 1 (119)}$ as $\sqrt{- 1} \cdot \sqrt{119}$ .

$x = \frac{- 1 \pm \sqrt{- 1} \cdot \sqrt{119}}{2 \cdot 3}$

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

$x = \frac{- 1 \pm i \sqrt{119}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{- 1 \pm i \sqrt{119}}{6}$