Solve using the Square Root Property 5y^2+12=4y

$5 y^{2} + 12 = 4 y$

Subtract $4 y$ from both sides of the equation.

$5 y^{2} + 12 - 4 y = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 5$ , $b = - 4$ , and $c = 12$ into the quadratic formula and solve for $y$ .

$\frac{4 \pm \sqrt{{(- 4)}^{2} - 4 \cdot (5 \cdot 12)}}{2 \cdot 5}$

Simplify.

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Simplify the numerator.

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Raise $- 4$ to the power of $2$ .

$y = \frac{4 \pm \sqrt{16 - 4 \cdot (5 \cdot 12)}}{2 \cdot 5}$

Multiply $5$ by $12$ .

$y = \frac{4 \pm \sqrt{16 - 4 \cdot 60}}{2 \cdot 5}$

Multiply $- 4$ by $60$ .

$y = \frac{4 \pm \sqrt{16 - 240}}{2 \cdot 5}$

Subtract $240$ from $16$ .

$y = \frac{4 \pm \sqrt{- 224}}{2 \cdot 5}$

Rewrite $- 224$ as $- 1 (224)$ .

$y = \frac{4 \pm \sqrt{- 1 \cdot 224}}{2 \cdot 5}$

Rewrite $\sqrt{- 1 (224)}$ as $\sqrt{- 1} \cdot \sqrt{224}$ .

$y = \frac{4 \pm \sqrt{- 1} \cdot \sqrt{224}}{2 \cdot 5}$

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

$y = \frac{4 \pm i \cdot \sqrt{224}}{2 \cdot 5}$

Rewrite $224$ as $4^{2} \cdot 14$ .

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Factor $16$ out of $224$ .

$y = \frac{4 \pm i \cdot \sqrt{16 (14)}}{2 \cdot 5}$

Rewrite $16$ as $4^{2}$ .

$y = \frac{4 \pm i \cdot \sqrt{4^{2} \cdot 14}}{2 \cdot 5}$

Pull terms out from under the radical.

$y = \frac{4 \pm i \cdot (4 \sqrt{14})}{2 \cdot 5}$

Move $4$ to the left of $i$ .

$y = \frac{4 \pm 4 i \sqrt{14}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$y = \frac{4 \pm 4 i \sqrt{14}}{10}$

Simplify $\frac{4 \pm 4 i \sqrt{14}}{10}$ .

$y = \frac{2 \pm 2 i \sqrt{14}}{5}$

Simplify the expression to solve for the $+$ portion of the $\pm$ .

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Simplify the numerator.

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Raise $- 4$ to the power of $2$ .

$y = \frac{4 \pm \sqrt{16 - 4 \cdot (5 \cdot 12)}}{2 \cdot 5}$

Multiply $5$ by $12$ .

$y = \frac{4 \pm \sqrt{16 - 4 \cdot 60}}{2 \cdot 5}$

Multiply $- 4$ by $60$ .

$y = \frac{4 \pm \sqrt{16 - 240}}{2 \cdot 5}$

Subtract $240$ from $16$ .

$y = \frac{4 \pm \sqrt{- 224}}{2 \cdot 5}$

Rewrite $- 224$ as $- 1 (224)$ .

$y = \frac{4 \pm \sqrt{- 1 \cdot 224}}{2 \cdot 5}$

Rewrite $\sqrt{- 1 (224)}$ as $\sqrt{- 1} \cdot \sqrt{224}$ .

$y = \frac{4 \pm \sqrt{- 1} \cdot \sqrt{224}}{2 \cdot 5}$

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

$y = \frac{4 \pm i \cdot \sqrt{224}}{2 \cdot 5}$

Rewrite $224$ as $4^{2} \cdot 14$ .

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Factor $16$ out of $224$ .

$y = \frac{4 \pm i \cdot \sqrt{16 (14)}}{2 \cdot 5}$

Rewrite $16$ as $4^{2}$ .

$y = \frac{4 \pm i \cdot \sqrt{4^{2} \cdot 14}}{2 \cdot 5}$

Pull terms out from under the radical.

$y = \frac{4 \pm i \cdot (4 \sqrt{14})}{2 \cdot 5}$

Move $4$ to the left of $i$ .

$y = \frac{4 \pm 4 i \sqrt{14}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$y = \frac{4 \pm 4 i \sqrt{14}}{10}$

Simplify $\frac{4 \pm 4 i \sqrt{14}}{10}$ .

$y = \frac{2 \pm 2 i \sqrt{14}}{5}$

Change the $\pm$ to $+$ .

$y = \frac{2 + 2 i \sqrt{14}}{5}$

Simplify the expression to solve for the $-$ portion of the $\pm$ .

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Simplify the numerator.

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Raise $- 4$ to the power of $2$ .

$y = \frac{4 \pm \sqrt{16 - 4 \cdot (5 \cdot 12)}}{2 \cdot 5}$

Multiply $5$ by $12$ .

$y = \frac{4 \pm \sqrt{16 - 4 \cdot 60}}{2 \cdot 5}$

Multiply $- 4$ by $60$ .

$y = \frac{4 \pm \sqrt{16 - 240}}{2 \cdot 5}$

Subtract $240$ from $16$ .

$y = \frac{4 \pm \sqrt{- 224}}{2 \cdot 5}$

Rewrite $- 224$ as $- 1 (224)$ .

$y = \frac{4 \pm \sqrt{- 1 \cdot 224}}{2 \cdot 5}$

Rewrite $\sqrt{- 1 (224)}$ as $\sqrt{- 1} \cdot \sqrt{224}$ .

$y = \frac{4 \pm \sqrt{- 1} \cdot \sqrt{224}}{2 \cdot 5}$

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

$y = \frac{4 \pm i \cdot \sqrt{224}}{2 \cdot 5}$

Rewrite $224$ as $4^{2} \cdot 14$ .

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Factor $16$ out of $224$ .

$y = \frac{4 \pm i \cdot \sqrt{16 (14)}}{2 \cdot 5}$

Rewrite $16$ as $4^{2}$ .

$y = \frac{4 \pm i \cdot \sqrt{4^{2} \cdot 14}}{2 \cdot 5}$

Pull terms out from under the radical.

$y = \frac{4 \pm i \cdot (4 \sqrt{14})}{2 \cdot 5}$

Move $4$ to the left of $i$ .

$y = \frac{4 \pm 4 i \sqrt{14}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$y = \frac{4 \pm 4 i \sqrt{14}}{10}$

Simplify $\frac{4 \pm 4 i \sqrt{14}}{10}$ .

$y = \frac{2 \pm 2 i \sqrt{14}}{5}$

Change the $\pm$ to $-$ .

$y = \frac{2 - 2 i \sqrt{14}}{5}$

The final answer is the combination of both solutions.

$y = \frac{2 + 2 i \sqrt{14}}{5}, \frac{2 - 2 i \sqrt{14}}{5}$

Solve using the Square Root Property 5y^2+12=4y

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