Solve Using the Quadratic Formula 4y^2-y+2=0

$4 y^{2} - y + 2 = 0$

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 $a = 4$ , $b = - 1$ , and $c = 2$ into the quadratic formula and solve for $y$ .

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

Step 3

Simplify.

Simplify the numerator.

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

$y = \frac{1 \pm \sqrt{1 - 4 \cdot 4 \cdot 2}}{2 \cdot 4}$

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

Multiply $- 4$ by $4$ .

$y = \frac{1 \pm \sqrt{1 - 16 \cdot 2}}{2 \cdot 4}$

Multiply $- 16$ by $2$ .

$y = \frac{1 \pm \sqrt{1 - 32}}{2 \cdot 4}$

Subtract $32$ from $1$ .

$y = \frac{1 \pm \sqrt{- 31}}{2 \cdot 4}$

Rewrite $- 31$ as $- 1 (31)$ .

$y = \frac{1 \pm \sqrt{- 1 \cdot 31}}{2 \cdot 4}$

Rewrite $\sqrt{- 1 (31)}$ as $\sqrt{- 1} \cdot \sqrt{31}$ .

$y = \frac{1 \pm \sqrt{- 1} \cdot \sqrt{31}}{2 \cdot 4}$

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

$y = \frac{1 \pm i \sqrt{31}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$y = \frac{1 \pm i \sqrt{31}}{8}$