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

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

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 $a = 5$ , $b = - 1$ , and $c = 6$ into the quadratic formula and solve for $x$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (5 \cdot 6)}}{2 \cdot 5}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 1$ to the power of $2$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot 5 \cdot 6}}{2 \cdot 5}$

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

Multiply $- 4$ by $5$ .

$x = \frac{1 \pm \sqrt{1 - 20 \cdot 6}}{2 \cdot 5}$

Multiply $- 20$ by $6$ .

$x = \frac{1 \pm \sqrt{1 - 120}}{2 \cdot 5}$

Subtract $120$ from $1$ .

$x = \frac{1 \pm \sqrt{- 119}}{2 \cdot 5}$

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

$x = \frac{1 \pm \sqrt{- 1 \cdot 119}}{2 \cdot 5}$

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

$x = \frac{1 \pm \sqrt{- 1} \cdot \sqrt{119}}{2 \cdot 5}$

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

$x = \frac{1 \pm i \sqrt{119}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{1 \pm i \sqrt{119}}{10}$