Solve Using the Quadratic Formula 2/7y^2+3/7y+2/7=0

$\frac{2}{7} y^{2} + \frac{3}{7} y + \frac{2}{7} = 0$

Step 1

Simplify the left side.

Simplify each term.

Combine $\frac{2}{7}$ and $y^{2}$ .

$\frac{2 y^{2}}{7} + \frac{3}{7} y + \frac{2}{7} = 0$

Combine $\frac{3}{7}$ and $y$ .

$\frac{2 y^{2}}{7} + \frac{3 y}{7} + \frac{2}{7} = 0$

Step 2

Multiply through by the least common denominator $7$ , then simplify.

Apply the distributive property.

$7 (\frac{2 y^{2}}{7}) + 7 (\frac{3 y}{7}) + 7 (\frac{2}{7}) = 0$

Simplify.

Cancel the common factor of $7$ .

Cancel the common factor.

$7 (\frac{2 y^{2}}{7}) + 7 (\frac{3 y}{7}) + 7 (\frac{2}{7}) = 0$

Rewrite the expression.

$2 y^{2} + 7 (\frac{3 y}{7}) + 7 (\frac{2}{7}) = 0$

Cancel the common factor of $7$ .

Cancel the common factor.

$2 y^{2} + 7 (\frac{3 y}{7}) + 7 (\frac{2}{7}) = 0$

Rewrite the expression.

$2 y^{2} + 3 y + 7 (\frac{2}{7}) = 0$

Cancel the common factor of $7$ .

Cancel the common factor.

$2 y^{2} + 3 y + 7 (\frac{2}{7}) = 0$

Rewrite the expression.

$2 y^{2} + 3 y + 2 = 0$

Step 3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4

Substitute the values $a = 2$ , $b = 3$ , and $c = 2$ into the quadratic formula and solve for $y$ .

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

Step 5

Simplify.

Simplify the numerator.

Raise $3$ to the power of $2$ .

$y = \frac{- 3 \pm \sqrt{9 - 4 \cdot 2 \cdot 2}}{2 \cdot 2}$

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

Multiply $- 4$ by $2$ .

$y = \frac{- 3 \pm \sqrt{9 - 8 \cdot 2}}{2 \cdot 2}$

Multiply $- 8$ by $2$ .

$y = \frac{- 3 \pm \sqrt{9 - 16}}{2 \cdot 2}$

Subtract $16$ from $9$ .

$y = \frac{- 3 \pm \sqrt{- 7}}{2 \cdot 2}$

Rewrite $- 7$ as $- 1 (7)$ .

$y = \frac{- 3 \pm \sqrt{- 1 \cdot 7}}{2 \cdot 2}$

Rewrite $\sqrt{- 1 (7)}$ as $\sqrt{- 1} \cdot \sqrt{7}$ .

$y = \frac{- 3 \pm \sqrt{- 1} \cdot \sqrt{7}}{2 \cdot 2}$

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

$y = \frac{- 3 \pm i \sqrt{7}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$y = \frac{- 3 \pm i \sqrt{7}}{4}$

Solve Using the Quadratic Formula 2/7y^2+3/7y+2/7=0

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